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340,094 | https://en.wikipedia.org/wiki/Estimated%20time%20of%20arrival | The estimated time of arrival (ETA) is the time when a ship, vehicle, aircraft, cargo, person, or emergency service is expected to arrive at a certain place.
Overview
One of the more common uses of the phrase is in public transportation where the movements of trains, buses, airplanes and the like can be used to generate estimated times of arrival depending on either a static timetable or through measurements on traffic intensity. In this respect, the phrase or its abbreviation is often paired with its complement, estimated time of departure (ETD), to indicate the expected start time of a particular journey. This information is often conveyed to a passenger information system as part of the core functionality of intelligent transportation systems.
For example, a certain flight may have a calculated ETA based on the speed by which it has covered the distance traveled so far. The remaining distance is divided by the speed previously measured to roughly estimate the arrival time. This particular method does not take into account any unexpected events (such as new wind directions) which may occur on the way to the flight's destination.
ETA is also used metaphorically in situations where nothing actually moves physically, as in describing the time estimated for a certain task to complete (e.g. work undertaken by an individual; a computation undertaken by a computer program; or a process undertaken by an organization). The associated term is "estimated time of accomplishment", which may be a backronym.
Applications
Accurate and timely estimations of times of arrival are important in several application areas:
In air traffic control arrival sequencing and scheduling, where scheduling aircraft arrival according to the first-come-first-served order of ETA at the runway minimizes delays.
In airport gate assignment methods, to optimize gate utilization.
In elevator control, to minimize the average waiting time or journey time of passengers (destination dispatch).
References
Time
Airline tickets
Passenger rail transport | Estimated time of arrival | [
"Physics",
"Mathematics"
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"Time",
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340,136 | https://en.wikipedia.org/wiki/Bernstein%20polynomial | In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician Sergei Natanovich Bernstein.
Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves.
A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm.
Definition
Bernstein basis polynomials
The n+1 Bernstein basis polynomials of degree n are defined as
where is a binomial coefficient.
So, for example,
The first few Bernstein basis polynomials for blending 1, 2, 3 or 4 values together are:
The Bernstein basis polynomials of degree n form a basis for the vector space of polynomials of degree at most n with real coefficients.
Bernstein polynomials
A linear combination of Bernstein basis polynomials
is called a Bernstein polynomial or polynomial in Bernstein form of degree n. The coefficients are called Bernstein coefficients or Bézier coefficients.
The first few Bernstein basis polynomials from above in monomial form are:
Properties
The Bernstein basis polynomials have the following properties:
, if or
for
and where is the Kronecker delta function:
has a root with multiplicity at point (note: if , there is no root at 0).
has a root with multiplicity at point (note: if , there is no root at 1).
The derivative can be written as a combination of two polynomials of lower degree:
The k-th derivative at 0:
The k-th derivative at 1:
The transformation of the Bernstein polynomial to monomials is and by the inverse binomial transformation, the reverse transformation is
The indefinite integral is given by
The definite integral is constant for a given n:
If , then has a unique local maximum on the interval at . This maximum takes the value
The Bernstein basis polynomials of degree form a partition of unity:
By taking the first -derivative of , treating as constant, then substituting the value , it can be shown that
Similarly the second -derivative of , with again then substituted , shows that
A Bernstein polynomial can always be written as a linear combination of polynomials of higher degree:
The expansion of the Chebyshev Polynomials of the First Kind into the Bernstein basis is
Approximating continuous functions
Let ƒ be a continuous function on the interval [0, 1]. Consider the Bernstein polynomial
It can be shown that
uniformly on the interval [0, 1].
Bernstein polynomials thus provide one way to prove the Weierstrass approximation theorem that every real-valued continuous function on a real interval [a, b] can be uniformly approximated by polynomial functions over .
A more general statement for a function with continuous kth derivative is
where additionally
is an eigenvalue of Bn; the corresponding eigenfunction is a polynomial of degree k.
Probabilistic proof
This proof follows Bernstein's original proof of 1912. See also Feller (1966) or Koralov & Sinai (2007).
Motivation
We will first give intuition for Bernstein's original proof. A continuous function on a compact interval must be uniformly continuous. Thus, the value of any continuous function can be uniformly approximated by its value on some finite net of points in the interval. This consideration renders the approximation theorem intuitive, given that polynomials should be flexible enough to match (or nearly match) a finite number of pairs . To do so, we might (1) construct a function close to on a lattice, and then (2) smooth out the function outside the lattice to make a polynomial.
The probabilistic proof below simply provides a constructive method to create a polynomial which is approximately equal to on such a point lattice, given that "smoothing out" a function is not always trivial. Taking the expectation of a random variable with a simple distribution is a common way to smooth. Here, we take advantage of the fact that Bernstein polynomials look like Binomial expectations. We split the interval into a lattice of n discrete values. Then, to evaluate any f(x), we evaluate f at one of the n lattice points close to x, randomly chosen by the Binomial distribution. The expectation of this approximation technique is polynomial, as it is the expectation of a function of a binomial RV. The proof below illustrates that this achieves a uniform approximation of f. The crux of the proof is to (1) justify replacing an arbitrary point with a binomially chosen lattice point by concentration properties of a Binomial distribution, and (2) justify the inference from to by uniform continuity.
Bernstein's proof
Suppose K is a random variable distributed as the number of successes in n independent Bernoulli trials with probability x of success on each trial; in other words, K has a binomial distribution with parameters n and x. Then we have the expected value and
By the weak law of large numbers of probability theory,
for every δ > 0. Moreover, this relation holds uniformly in x, which can be seen from its proof via Chebyshev's inequality, taking into account that the variance of K, equal to x(1−x), is bounded from above by irrespective of x.
Because ƒ, being continuous on a closed bounded interval, must be uniformly continuous on that interval, one infers a statement of the form
uniformly in x for each . Taking into account that ƒ is bounded (on the given interval) one finds that
uniformly in x. To justify this statement, we use a common method in probability theory to convert from closeness in probability to closeness in expectation. One splits the expectation of into two parts split based on whether or not . In the interval where the difference does not exceed ε, the expectation clearly cannot exceed ε.
In the other interval, the difference still cannot exceed 2M, where M is an upper bound for |ƒ(x)| (since uniformly continuous functions are bounded). However, by our 'closeness in probability' statement, this interval cannot have probability greater than ε. Thus, this part of the expectation contributes no more than 2M times ε. Then the total expectation is no more than , which can be made arbitrarily small by choosing small ε.
Finally, one observes that the absolute value of the difference between expectations never exceeds the expectation of the absolute value of the difference, a consequence of Holder's Inequality. Thus, using the above expectation, we see that (uniformly in x)
Noting that our randomness was over K while x is constant, the expectation of f(x) is just equal to f(x). But then we have shown that converges to f(x). Then we will be done if is a polynomial in x (the subscript reminding us that x controls the distribution of K). Indeed it is:
Uniform convergence rates between functions
In the above proof, recall that convergence in each limit involving f depends on the uniform continuity of f, which implies a rate of convergence dependent on f 's modulus of continuity It also depends on 'M', the absolute bound of the function, although this can be bypassed if one bounds and the interval size. Thus, the approximation only holds uniformly across x for a fixed f, but one can readily extend the proof to uniformly approximate a set of functions with a set of Bernstein polynomials in the context of equicontinuity.
Elementary proof
The probabilistic proof can also be rephrased in an elementary way, using the underlying probabilistic ideas but proceeding by direct verification:
The following identities can be verified:
("probability")
("mean")
("variance")
In fact, by the binomial theorem
and this equation can be applied twice to . The identities (1), (2), and (3) follow easily using the substitution .
Within these three identities, use the above basis polynomial notation
and let
Thus, by identity (1)
so that
Since f is uniformly continuous, given , there is a such that whenever
. Moreover, by continuity, . But then
The first sum is less than ε. On the other hand, by identity (3) above, and since , the second sum is bounded by times
(Chebyshev's inequality)
It follows that the polynomials fn tend to f uniformly.
Generalizations to higher dimension
Bernstein polynomials can be generalized to dimensions – the resulting polynomials have the form . In the simplest case only products of the unit interval are considered; but, using affine transformations of the line, Bernstein polynomials can also be defined for products . For a continuous function on the -fold product of the unit interval, the proof that can be uniformly approximated by
is a straightforward extension of Bernstein's proof in one dimension.
See also
Polynomial interpolation
Newton form
Lagrange form
Binomial QMF (also known as Daubechies wavelet)
Notes
References
, English translation
, Russian edition first published in 1940
External links
from University of California, Davis. Note the error in the summation limits in the first formula on page 9.
Feature Column from American Mathematical Society
Numerical analysis
Polynomials
Articles containing proofs | Bernstein polynomial | [
"Mathematics"
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340,198 | https://en.wikipedia.org/wiki/Pointwise%20convergence | In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared.
Definition
Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as
if (and only if) the limit of the sequence evaluated at each point in the domain of is equal to , written as
The function is said to be the pointwise limit function of the
The definition easily generalizes from sequences to nets . We say converge pointwises to , written as
if (and only if) is the unique accumulation point of the net evaluated at each point in the domain of , written as
Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
Properties
This concept is often contrasted with uniform convergence. To say that
means that
where is the common domain of and , and stands for the supremum. That is a stronger statement than the assertion of pointwise convergence: every uniformly convergent sequence is pointwise convergent, to the same limiting function, but some pointwise convergent sequences are not uniformly convergent. For example, if is a sequence of functions defined by then pointwise on the interval but not uniformly.
The pointwise limit of a sequence of continuous functions may be a discontinuous function, but only if the convergence is not uniform. For example,
takes the value when is an integer and when is not an integer, and so is discontinuous at every integer.
The values of the functions need not be real numbers, but may be in any topological space, in order that the concept of pointwise convergence make sense. Uniform convergence, on the other hand, does not make sense for functions taking values in topological spaces generally, but makes sense for functions taking values in metric spaces, and, more generally, in uniform spaces.
Topology
Let denote the set of all functions from some given set into some topological space
As described in the article on characterizations of the category of topological spaces, if certain conditions are met then it is possible to define a unique topology on a set in terms of which nets do and do not converge.
The definition of pointwise convergence meets these conditions and so it induces a topology, called the , on the set of all functions of the form
A net in converges in this topology if and only if it converges pointwise.
The topology of pointwise convergence is the same as convergence in the product topology on the space where is the domain and is the codomain.
Explicitly, if is a set of functions from some set into some topological space then the topology of pointwise convergence on is equal to the subspace topology that it inherits from the product space when is identified as a subset of this Cartesian product via the canonical inclusion map defined by
If the codomain is compact, then by Tychonoff's theorem, the space is also compact.
Almost everywhere convergence
In measure theory, one talks about almost everywhere convergence of a sequence of measurable functions defined on a measurable space. That means pointwise convergence almost everywhere, that is, on a subset of the domain whose complement has measure zero. Egorov's theorem states that pointwise convergence almost everywhere on a set of finite measure implies uniform convergence on a slightly smaller set.
Almost everywhere pointwise convergence on the space of functions on a measure space does not define the structure of a topology on the space of measurable functions on a measure space (although it is a convergence structure). For in a topological space, when every subsequence of a sequence has itself a subsequence with the same subsequential limit, the sequence itself must converge to that limit.
But consider the sequence of so-called "galloping rectangles" functions, which are defined using the floor function: let and mod and let
Then any subsequence of the sequence has a sub-subsequence which itself converges almost everywhere to zero, for example, the subsequence of functions which do not vanish at But at no point does the original sequence converge pointwise to zero. Hence, unlike convergence in measure and convergence, pointwise convergence almost everywhere is not the convergence of any topology on the space of functions.
See also
References
Convergence (mathematics)
Measure theory
Topological spaces
Topology of function spaces
hu:Függvénysorozatok konvergenciája#Pontonkénti konvergencia | Pointwise convergence | [
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340,201 | https://en.wikipedia.org/wiki/Soundproofing | Soundproofing is any means of impeding sound propagation. There are several methods employed including increasing the distance between the source and receiver, decoupling, using noise barriers to reflect or absorb the energy of the sound waves, using damping structures such as sound baffles for absorption, or using active antinoise sound generators.
Acoustic quieting and noise control can be used to limit unwanted noise. Soundproofing can reduce the transmission of unwanted direct sound waves from the source to an involuntary listener through the use of distance and intervening objects in the sound path (see sound transmission class and sound reduction index).
Soundproofing can suppress unwanted indirect sound waves such as reflections that cause echoes and resonances that cause reverberation.
Techniques
Absorption
Sound-absorbing material controls reverberant sound pressure levels within a cavity, enclosure or room. Synthetic absorption materials are porous, referring to open cell foam (acoustic foam, soundproof foam). Fibrous absorption material such as cellulose, mineral wool, fiberglass, sheep's wool, are more commonly used to deaden resonant frequencies within a cavity (wall, floor, or ceiling insulation), serving a dual purpose along with their thermal insulation properties. Both fibrous and porous absorption material are used to create acoustic panels, which absorb sound reflections in a room, improving speech intelligibility.
Porous absorbers
Porous absorbers, typically open cell rubber foams or melamine sponges, absorb noise by friction within the cell structure. Porous open cell foams are highly effective noise absorbers across a broad range of medium-high frequencies. Performance can be less impressive at lower frequencies. The exact absorption profile of a porous open-cell foam will be determined by a number of factors including cell size, tortuosity, porosity, thickness, and density.
The absorption aspect in soundproofing should not be confused with sound-absorbing panels used in acoustic treatments. Absorption in this sense refers to reducing a resonating frequency in a cavity by installing insulation between walls, ceilings or floors. Acoustic panels can play a role in treatment reducing reflections that make the overall sound in the source room louder, after walls, ceilings, and floors have been soundproofed.
Resonant absorbers
Resonant panels, Helmholtz resonators and other resonant absorbers work by damping a sound wave as they reflect it. Unlike porous absorbers, resonant absorbers are most effective at low-medium frequencies and the absorption of resonant absorbers is matched to a narrow frequency range.
Damping
Damping serves to reduce resonance in the room, by absorption or redirection through reflection or diffusion. Absorption reduces the overall sound level, whereas redirection makes unwanted sound harmless or even beneficial by reducing coherence. Damping can be separately applied to reduce the acoustic resonance in the air or to reduce mechanical resonance in the structure of the room itself or things in the room.
Decoupling
Creating separation between a sound source and any form of adjoining mass, hindering the direct pathway for sound transfer.
Distance
The energy density of sound waves decreases as they become farther apart so increasing the distance between the receiver and source results in a progressively lesser intensity of sound at the receiver. In a normal three-dimensional setting, with a point source and point receptor, the intensity of sound waves will be attenuated according to the inverse square of the distance from the source.
Mass
Adding dense material to treatment helps stop sound waves from exiting a source wall, ceiling or floor. Materials include mass-loaded vinyl, soundproof sheetrock or drywall, plywood, fibreboard, concrete or rubber. Different widths and densities in soundproofing material reduce sound within a variable frequency range.
Reflection
When sound waves hit a medium, the reflection of that sound is dependent on the dissimilarity of the material it comes in contact with. Sound hitting a concrete surface will result in a much different reflection than if the sound were to hit a softer medium such as fiberglass. In an outdoor environment such as highway engineering, embankments or paneling are often used to reflect sound upwards into the sky.
Diffusion
If a specular reflection from a hard flat surface is giving a problematic echo then an acoustic diffuser may be applied to the surface. It will scatter sound in all directions.
Active noise control
In active noise control, a microphone is used to pick up the sound that is then analyzed by a computer; then, sound waves with opposite polarity (180° phase at all frequencies) are output through a speaker, causing destructive interference and canceling much of the noise.
Applications
Residential
Residential sound programs aim to decrease or eliminate the effects of exterior noise. The main focus of a residential sound program in existing structures is the windows and doors. Solid wood doors are a better sound barrier than hollow doors. Curtains can be used to dampen sound, either through use of heavy materials or through the use of air chambers known as honeycombs. Single-, double- and triple-honeycomb designs achieve relatively greater degrees of sound damping. The primary soundproofing limit of curtains is the lack of a seal at the edge of the curtain, although this may be alleviated with the use of sealing features, such as hook and loop fastener, adhesive, magnets, or other materials. The thickness of glass will play a role when diagnosing sound leakage. Double-pane windows achieve somewhat greater sound damping than single-pane windows when well-sealed into the opening of the window frame and wall.
Significant noise reduction can also be achieved by installing a second interior window. In this case, the exterior window remains in place while a slider or hung window is installed within the same wall openings.
In the US, the FAA offers sound-reducing for homes that fall within a noise contour where the average sound level is or greater. It is part of their Residential Sound Insulation Program. The program provides solid-core wood entry doors plus windows and storm doors.
Ceilings
Sealing gaps and cracks around electrical wiring, water pipes and ductwork using acoustical caulk or spray foam will significantly reduce unwanted noise as a preliminary step for ceiling soundproofing. Acoustical caulk should be used along the perimeter of the wall and around all fixtures and duct registers to further seal the treatment. Mineral wool insulation is most commonly used in soundproofing for its density and low cost compared to other soundproofing materials. Spray foam insulation should only be used to fill gaps and cracks or as a 1-2 inch layer before installing mineral wool. Cured spray foam and other closed-cell foam can be a sound conductor. Spray foam is not porous enough to absorb sound and is also not dense enough to stop sound.
An effective method to reduce impact noise is the "resilient isolation channel". The channels decouple the drywall from the joists, reducing the transfer of vibration.
Walls
Mass is the only way to stop sound. Mass refers to drywall, plywood or concrete. Mass-loaded vinyl (MLV) is used to dampen or weaken sound waves between layers of mass. Use of a viscoelastic damping compound or MLV converts sound waves into heat, weakening the waves before they reach the next layer of mass. It is important to use multiple layers of mass, in different widths and densities, to optimize any given soundproofing treatment. Installing soundproof drywall is recommended for its higher sound transmission class (STC) value. Soundproof drywall in combination with a viscoelastic compound may achieve a noise reduction of STC 60+.
Walls are filled with mineral wool insulation. Depending on the desired level of treatment, two layers of insulation may be required. Outlets, light switches, and electrical boxes are weak points in any given soundproofing treatment. Electrical boxes should be wrapped in clay or putty and backed with MLV. After switch plates, outlet covers and lights are installed, acoustical caulking should be applied around the perimeter of the plates or fixtures.
Floors
Decoupling between the joist and subfloor plywood using neoprene joist tape or u-shaped rubber spacers helps create soundproof flooring. An additional layer of plywood can be installed with a viscoelastic compound. Mass loaded vinyl, in combination with open-cell rubber or a closed-cell foam floor underlayment, will further reduce sound transmission. After applying these techniques, hardwood flooring or carpeting can be installed. Additional area rugs and furniture will help reduce unwanted reflection within the room.
Room within a room
A room within a room (RWAR) is one method of isolating sound and preventing it from transmitting to the outside world where it may be undesirable.
Most sound transfer from a room to the outside occurs through mechanical means. The vibration passes directly through the brick, woodwork and other solid structural elements. When it meets with an element such as a wall, ceiling, floor or window, which acts as a sounding board, the vibration is amplified and heard in the second space. A mechanical transmission is much faster, more efficient and more readily amplified than an airborne transmission of the same initial strength.
The use of acoustic foam and other absorbent means is less effective against this transmitted vibration. The transmission can be stopped by breaking the connection between the room that contains the noise source and the outside world. This is called acoustic decoupling.
Commercial
Restaurants, schools, office businesses, and healthcare facilities use architectural acoustics to reduce noise for their customers. In the United States, OSHA has requirements regulating the length of exposure of workers to certain levels of noise.
For educators and students, improving the sound quality of an environment will subsequently improve student learning, concentration, and teacher-student inter-communications. In 2014, a research study conducted by Applied Science revealed 86% of students perceived their instructors more intelligibly, while 66% of students reported experiencing higher concentration levels after sound-absorbing materials were incorporated into the classroom.
Automotive
Automotive soundproofing aims to decrease or eliminate the effects of exterior noise, primarily engine, exhaust and tire noise across a wide frequency range. A panel damping material is fitted which reduces the vibration of the vehicle's body panels when they are excited by one of the many high-energy sound sources in play when the vehicle is in use. There are many complex noises created within vehicles which change with the driving environment and speed at which the vehicle travels. Significant noise reductions of up to 8 dB can be achieved by installing a combination of different types of materials.
The automotive environment limits the thickness of materials that can be used, but combinations of dampers, barriers, and absorbers are common. Common materials include felt, foam, polyester, and polypropylene blend materials. Waterproofing may be necessary depending on the materials used. Acoustic foam can be applied in different areas of a vehicle during manufacture to reduce cabin noise. Foams also have cost and performance advantages in installation since foam material can expand and fill cavities after application and also prevent leaks and some gases from entering the vehicle. Vehicle soundproofing can reduce wind, engine, road, and tire noise. Vehicle soundproofing can reduce sound inside a vehicle from five to 20 decibels.
Surface-damping materials are very effective at reducing structure-borne noise. Passive damping materials have been used since the early 1960s in the aerospace industry. Over the years, advances in material manufacturing and the development of more efficient analytical and experimental tools to characterize complex dynamic behaviors enabled the expansion of the usage of these materials to the automotive industry. Nowadays, multiple viscoelastic damping pads are usually attached to the body in order to attenuate higher-order structural panel modes that significantly contribute to the overall noise level inside the cabin. Traditionally, experimental techniques are used to optimize the size and location of damping treatments. In particular, laser vibrometer-type tests are often conducted on the body in white structures enabling the fast acquisition of a large number of measurement points with a good spatial resolution. However, testing a complete vehicle is mostly infeasible, requiring evaluation of every subsystem individually, hence limiting the usability of this technology in a fast and efficient way. Alternatively, structural vibrations can also be acoustically measured using particle velocity sensors located near a vibrating structure. Several studies have revealed the potential of particle velocity sensors for characterizing structural vibrations, which accelerates the entire testing process when combined with scanning techniques.
Noise barriers
Since the early 1970s, it has become common practice in the United States and other industrialized countries to engineer noise barriers along major highways to protect adjacent residents from intruding roadway noise. The Federal Highway Administration (FHWA) in conjunction with State Highway Administration (SHA) adopted Federal Regulation (23 CFR 772) requiring each state to adopt their own policy in regards to abatement of highway traffic noise. Engineering techniques have been developed to predict an effective geometry for the noise barrier design in a particular real-world situation. Noise barriers may be constructed of wood, masonry, earth or a combination thereof.
See also
Acoustic transmission
Acoustiblok
Hearing test
Noise pollution
Noise regulation
Recording studio
References
Acoustics
Fluid dynamics
Noise reduction
Sound
Noise control | Soundproofing | [
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] | 2,705 | [
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340,238 | https://en.wikipedia.org/wiki/Occasionalism | Occasionalism is a philosophical doctrine about causation which says that created substances cannot be efficient causes of events. Instead, all events are taken to be caused directly by God. (A related concept, which has been called "occasional causation", also denies a link of efficient causation between mundane events, but may differ as to the identity of the true cause that replaces them.) The doctrine states that the illusion of efficient causation between mundane events arises out of God's causing of one event after another. However, there is no necessary connection between the two: it is not that the first event causes God to cause the second event: rather, God first causes one and then causes the other.
Islamic theological schools
The doctrine first reached prominence in the Islamic theological schools of Iraq, especially in Basra. The ninth century theologian Abu al-Hasan al-Ash'ari argued that there is no Secondary Causation in the created order. The world is sustained and governed through direct intervention of a divine primary causation. As such the world is in a constant state of recreation by God. In the Arabic language this was known as Kasb.
The most famous proponent of the Asharite occasionalist doctrine was Abu Hamid Muhammad ibn Muhammad al-Ghazali, an 11th-century theologian based in Baghdad. In The Incoherence of the Philosophers, Al-Ghazali launched a philosophical critique against Neoplatonic-influenced early Islamic philosophers such as Al-Farabi and Ibn Sina. In response to the philosophers' claim that the created order is governed by secondary efficient causes (God being, as it were, the Primary and Final Cause in an ontological and logical sense), Ghazali argues that what we observe as regularity in nature based presumably upon some natural law is actually a kind of constant and continual regularity. There is no independent necessitation of change and becoming, other than what God has ordained. To posit an independent causality outside of God's knowledge and action is to deprive him of true agency, and diminish his attribute of power. In his famous example, when fire and cotton are placed in contact, the cotton is burned not because of the heat of the fire, but through God's direct intervention, a claim which he defended using logic. In the 12th century, the Islamic theologian Fakhr al-Din al-Razi expounded upon similar theories of occasionalism in his works.
Because God is usually seen as rational, rather than arbitrary, his behaviour in normally causing events in the same sequence (i.e., what appears to us to be efficient causation) can be understood as a natural outworking of that principle of reason, which we then describe as the laws of nature. Properly speaking, however, these are not laws of nature but laws by which God chooses to govern his own behaviour (his autonomy, in the strict sense) — in other words, his rational will. This is not, however, an essential element of an occasionalist account, and occasionalism can include positions where God's behaviour (and thus that of the world) is viewed as ultimately inscrutable, thus maintaining God's essential transcendence. On this understanding, apparent anomalies such as miracles are not really such: they are simply God behaving in a way that appears unusual to us. Given his transcendent freedom, he is not bound even by his own nature. Miracles, as breaks in the rational structure of the universe, can occur, since God's relationship with the world is not mediated by rational principles.
In a 1978 article in Studia Islamica, Lenn Goodman asks the question, "Did Al-Ghazâlî Deny Causality?" and demonstrates that Ghazali did not deny the existence of observed, "worldly" causation. According to Goodman's analysis, Ghazali does not claim that there is never any link between observed cause and observed effect: rather, Ghazali argues that there is no necessary link between observed cause and effect.
Dualism
One of the motivations for the theory is the dualist belief that mind and matter are so utterly different in their essences that one cannot affect the other. Thus, a person's mind cannot be the true cause of his hand's moving, nor can a physical wound be the true cause of mental anguish. In other words, the mental cannot cause the physical and vice versa. Also, occasionalists generally hold that the physical cannot cause the physical either, for no necessary connection can be perceived between physical causes and effects. The will of God is taken to be necessary.
The doctrine is, however, more usually associated with certain seventeenth century philosophers of the Cartesian school. There are hints of an occasionalist viewpoint here and there in Descartes's own writings, but these can mostly be explained away under alternative interpretations. However, many of his later followers quite explicitly committed themselves to an occasionalist position. In one form or another, the doctrine can be found in the writings of: Johannes Clauberg, Claude Clerselier, Gerauld de Cordemoy, Arnold Geulincx, Louis de La Forge, François Lamy, and (most notably) Nicolas Malebranche.
Hume's arguments, Berkeley and Leibniz
These occasionalists' negative argument, that no necessary connections could be discovered between mundane events, was anticipated by certain arguments of Nicholas of Autrecourt in the fourteenth century, and were later taken up by David Hume in the eighteenth century. Hume, however, stopped short when it came to the positive side of the theory, where God was called upon to replace such connections, complaining that "We are got into fairy land [...] Our line is too short to fathom such immense abysses." Instead, Hume felt that the only place to find necessary connections was in the subjective associations of ideas within the mind itself. George Berkeley was also inspired by the occasionalists, and he agreed with them that no efficient power could be attributed to bodies. For Berkeley, bodies merely existed as ideas in percipient minds, and all such ideas were, as he put it, "visibly inactive". However, Berkeley disagreed with the occasionalists by continuing to endow the created minds themselves with efficient power. Gottfried Wilhelm Leibniz agreed with the occasionalists that there could be no efficient causation between distinct created substances, but he did not think it followed that there was no efficient power in the created world at all. On the contrary, every simple substance had the power to produce changes in itself. The illusion of transient efficient causation, for Leibniz, arose out of the pre-established harmony between the alterations produced immanently within different substances. Leibniz means, that if God did not exist, "there would be nothing real in the possibilities, not only nothing existent, but also nothing possible".
Quantum mechanics
In 1993, Pierce College chemistry professor Karen Harding published the paper "Causality Then and Now: Al Ghazali and Quantum Theory" that described several "remarkable" similarities between Ghazali's concept of occasionalism and the widely accepted Copenhagen interpretation of quantum mechanics. She stated: "In both cases, and contrary to common sense, objects are viewed as having no inherent properties and no independent existence. In order for an object to exist, it must be brought into being either by God (al-Ghazali) or by an observer (the Copenhagen Interpretation)." She also stated:
Continuing from philosopher Graham Harman's work on occasionalism in the context of object-oriented ontology, Simon Weir proposed in 2020 an alternate view of the relationship between quantum theory and occasionalism opposed to the Copenhagen interpretation, where virtual particles act as one of many kinds of mediating sensual objects.
See also
Pre-established harmony
Providentialism
Psychophysical parallelism
Theological determinism
God the Sustainer
Notes
External links
Cosmological Argument aiming to establish Occasionalism
Occasionalism from the Catholic Encyclopedia
International Society for the Study of Occasionalism
Occasionalism article in the Internet Encyclopedia of Philosophy
Causality
Metaphysics of religion
Dualism (philosophy of mind)
Conceptions of God
Metaphysical theories | Occasionalism | [
"Physics"
] | 1,685 | [] |
340,240 | https://en.wikipedia.org/wiki/Partition%20of%20a%20set | In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.
Definition and notation
A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets).
Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold:
The family P does not contain the empty set (that is ).
The union of the sets in P is equal to X (that is ). The sets in P are said to exhaust or cover X. See also collectively exhaustive events and cover (topology).
The intersection of any two distinct sets in P is empty (that is ). The elements of P are said to be pairwise disjoint or mutually exclusive. See also mutual exclusivity.
The sets in are called the blocks, parts, or cells, of the partition. If then we represent the cell containing by . That is to say, is notation for the cell in which contains .
Every partition may be identified with an equivalence relation on , namely the relation such that for any we have if and only if (equivalently, if and only if ). The notation evokes the idea that the equivalence relation may be constructed from the partition. Conversely every equivalence relation may be identified with a partition. This is why it is sometimes said informally that "an equivalence relation is the same as a partition". If P is the partition identified with a given equivalence relation , then some authors write . This notation is suggestive of the idea that the partition is the set X divided in to cells. The notation also evokes the idea that, from the equivalence relation one may construct the partition.
The rank of is , if is finite.
Examples
The empty set has exactly one partition, namely . (Note: this is the partition, not a member of the partition.)
For any non-empty set X, P = is a partition of X, called the trivial partition.
Particularly, every singleton set {x} has exactly one partition, namely .
For any non-empty proper subset A of a set U, the set A together with its complement form a partition of U, namely, .
The set has these five partitions (one partition per item):
, sometimes written 1 | 2 | 3.
, or 1 2 | 3.
, or 1 3 | 2.
, or 1 | 2 3.
, or 123 (in contexts where there will be no confusion with the number).
The following are not partitions of :
is not a partition (of any set) because one of its elements is the empty set.
is not a partition (of any set) because the element 2 is contained in more than one block.
is not a partition of because none of its blocks contains 3; however, it is a partition of .
Partitions and equivalence relations
For any equivalence relation on a set X, the set of its equivalence classes is a partition of X. Conversely, from any partition P of X, we can define an equivalence relation on X by setting precisely when x and y are in the same part in P. Thus the notions of equivalence relation and partition are essentially equivalent.
The axiom of choice guarantees for any partition of a set X the existence of a subset of X containing exactly one element from each part of the partition. This implies that given an equivalence relation on a set one can select a canonical representative element from every equivalence class.
Refinement of partitions
A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that α ≤ ρ.
This "finer-than" relation on the set of partitions of X is a partial order (so the notation "≤" is appropriate). Each set of elements has a least upper bound (their "join") and a greatest lower bound (their "meet"), so that it forms a lattice, and more specifically (for partitions of a finite set) it is a geometric and supersolvable lattice. The partition lattice of a 4-element set has 15 elements and is depicted in the Hasse diagram on the left.
The meet and join of partitions α and ρ are defined as follows. The meet is the partition whose blocks are the intersections of a block of α and a block of ρ, except for the empty set. In other words, a block of is the intersection of a block of α and a block of ρ that are not disjoint from each other. To define the join , form a relation on the blocks A of α and the blocks B of ρ by A ~ B if A and B are not disjoint. Then is the partition in which each block C is the union of a family of blocks connected by this relation.
Based on the equivalence between geometric lattices and matroids, this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms of the lattice, namely, the partitions with singleton sets and one two-element set. These atomic partitions correspond one-for-one with the edges of a complete graph. The matroid closure of a set of atomic partitions is the finest common coarsening of them all; in graph-theoretic terms, it is the partition of the vertices of the complete graph into the connected components of the subgraph formed by the given set of edges. In this way, the lattice of partitions corresponds to the lattice of flats of the graphic matroid of the complete graph.
Another example illustrates refinement of partitions from the perspective of equivalence relations. If D is the set of cards in a standard 52-card deck, the same-color-as relation on D – which can be denoted ~C – has two equivalence classes: the sets {red cards} and {black cards}. The 2-part partition corresponding to ~C has a refinement that yields the same-suit-as relation ~S, which has the four equivalence classes {spades}, {diamonds}, {hearts}, and {clubs}.
Noncrossing partitions
A partition of the set N = {1, 2, ..., n} with corresponding equivalence relation ~ is noncrossing if it has the following property: If four elements a, b, c and d of N having a < b < c < d satisfy a ~ c and b ~ d, then a ~ b ~ c ~ d. The name comes from the following equivalent definition: Imagine the elements 1, 2, ..., n of N drawn as the n vertices of a regular n-gon (in counterclockwise order). A partition can then be visualized by drawing each block as a polygon (whose vertices are the elements of the block). The partition is then noncrossing if and only if these polygons do not intersect.
The lattice of noncrossing partitions of a finite set forms a subset of the lattice of all partitions, but not a sublattice, since the join operations of the two lattices do not agree.
The noncrossing partition lattice has taken on importance because of its role in free probability theory.
Counting partitions
The total number of partitions of an n-element set is the Bell number Bn. The first several Bell numbers are B0 = 1,
B1 = 1, B2 = 2, B3 = 5, B4 = 15, B5 = 52, and B6 = 203 . Bell numbers satisfy the recursion
and have the exponential generating function
The Bell numbers may also be computed using the Bell triangle
in which the first value in each row is copied from the end of the previous row, and subsequent values are computed by adding two numbers, the number to the left and the number to the above left of the position. The Bell numbers are repeated along both sides of this triangle. The numbers within the triangle count partitions in which a given element is the largest singleton.
The number of partitions of an n-element set into exactly k (non-empty) parts is the Stirling number of the second kind S(n, k).
The number of noncrossing partitions of an n-element set is the Catalan number
See also
Exact cover
Block design
Cluster analysis
List of partition topics
Lamination (topology)
MECE principle
Partial equivalence relation
Partition algebra
Partition refinement
Point-finite collection
Rhyme schemes by set partition
Weak ordering (ordered set partition)
Notes
References
Basic concepts in set theory
Combinatorics
Families of sets | Partition of a set | [
"Mathematics"
] | 1,888 | [
"Basic concepts in set theory",
"Families of sets",
"Discrete mathematics",
"Combinatorics"
] |
340,284 | https://en.wikipedia.org/wiki/Electron%20ionization | Electron ionization (EI, formerly known as electron impact ionization and electron bombardment ionization) is an ionization method in which energetic electrons interact with solid or gas phase atoms or molecules to produce ions. EI was one of the first ionization techniques developed for mass spectrometry. However, this method is still a popular ionization technique. This technique is considered a hard (high fragmentation) ionization method, since it uses highly energetic electrons to produce ions. This leads to extensive fragmentation, which can be helpful for structure determination of unknown compounds. EI is the most useful for organic compounds which have a molecular weight below 600 amu. Also, several other thermally stable and volatile compounds in solid, liquid and gas states can be detected with the use of this technique when coupled with various separation methods.
History
Electron ionization was first described in 1918 by Canadian-American Physicist Arthur J. Dempster in the article of "A new method of positive ray analysis." It was the first modern mass spectrometer and used positive rays to determine the ratio of the mass to charge of various constituents. In this method, the ion source used an electron beam directed at a solid surface. The anode was made cylindrical in shape using the metal which was to be studied. Subsequently, it was heated by a concentric coil and then was bombarded with electrons. Using this method, the two isotopes of lithium and three isotopes of magnesium, with their atomic weights and relative proportions, were able to be determined. Since then this technique has been used with further modifications and developments. The use of a focused monoenergetic beam of electrons for ionization of gas phase atoms and molecules was developed by Bleakney in 1929.
Principle of operation
In this process, an electron from the analyte molecule (M) is expelled during the collision process to convert the molecule to a positive ion with an odd number of electrons. The following gas phase reaction describes the electron ionization process
M{} + e^- -> M^{+\bullet}{} + 2e^-
where M is the analyte molecule being ionized, e− is the electron and M+• is the resulting molecular ion.
In an EI ion source, electrons are produced through thermionic emission by heating a wire filament that has electric current running through it. The kinetic energy of the bombarding electrons should have higher energy than the ionization energy of the sample molecule. The electrons are accelerated to 70 eV in the region between the filament and the entrance to the ion source block. The sample under investigation which contains the neutral molecules is introduced to the ion source in a perpendicular orientation to the electron beam. Close passage of highly energetic electrons in low pressure (ca. 10−5 to 10−6 torr) causes large fluctuations in the electric field around the neutral molecules and induces ionization and fragmentation. The fragmentation in electron ionization can be described using Born Oppenheimer potential curves as in the diagram. The red arrow shows the electron impact energy which is enough to remove an electron from the analyte and form a molecular ion from non- dissociative results. Due to the higher energy supplied by 70 eV electrons other than the molecular ion, several other bond dissociation reactions can be seen as dissociative results, shown by the blue arrow in the diagram. These ions are known as second-generation product ions. The radical cation products are then directed towards the mass analyzer by a repeller electrode. The ionization process often follows predictable cleavage reactions that give rise to fragment ions which, following detection and signal processing, convey structural information about the analyte.
The efficiency of EI
Increasing the electron ionization process is done by increasing the ionization efficiency. In order to achieve higher ionization efficiency there should be an optimized filament current, emission current, and ionizing current. The current supplied to the filament to heat it to incandescent is called the filament current. The emission current is the current measured between the filament and the electron entry slit. The ionizing current is the rate of electron arrival at the trap. It is a direct measure of the number of electrons in the chamber that are available for ionization.
The sample ion current (I+) is the measure of the ionization rate. This can be enhanced by manipulation of the ion extraction efficiency (β), the total ionizing cross section (Qi), the effective ionizing path length (L), the concentration of the sample molecules([N]) and the ionizing current (Ie). The equation can be shown as follows:
The ion extraction efficiency (β) can be optimized by increasing the voltage of both repeller and acceleration. Since the ionization cross section depends on the chemical nature of the sample and the energy of ionizing electrons a standard value of 70 eV is used. At low energies (around 20 eV), the interactions between the electrons and the analyte molecules do not transfer enough energy to cause ionization. At around 70 eV, the de Broglie wavelength of the electrons matches the length of typical bonds in organic molecules (about 0.14 nm) and energy transfer to organic analyte molecules is maximized, leading to the strongest possible ionization and fragmentation. Under these conditions, about 1 in 1000 analyte molecules in the source are ionized. At higher energies, the de Broglie wavelength of the electrons becomes smaller than the bond lengths in typical analytes; the molecules then become "transparent" to the electrons and ionization efficiency decreases. The effective ionizing path length (L) can be increased by using a weak magnetic field. But the most practical way to increase the sample current is to operate the ion source at higher ionizing current (Ie).
Instrumentation
A schematic diagram of instrumentation which can be used for electron ionization is shown to the right. The ion source block is made out of metal. As the electron source, the cathode, which can be a thin filament of tungsten or rhenium wire, is inserted through a slit to the source block. Then it is heated up to an incandescent temperature to emit electrons. A potential of 70 V is applied between the cathode and source block to accelerate them to 70 eV kinetic energy to produce positive ions. The potential of the anode (electron trap) is slightly positive and it is placed on the outside of the ionization chamber, directly opposite to the cathode. The unused electrons are collected by this electron trap. The sample is introduced through the sample hole. To increase the ionization process, a weak magnetic field is applied parallel to the direction of the electrons' travel. Because of this, electrons travel in a narrow helical path, which increases their path length. The positive ions that are generated are accelerated by the repeller electrode into the accelerating region through the slit in the source block. By applying a potential to the ion source and maintaining the exit slit at ground potential, ions enter the mass analyzer with a fixed kinetic energy. To avoid the condensation of the sample, the source block is heated to approximately 300 °C.
Applications
Since the early 20th century electron ionization has been one of the most popular ionization techniques because of the large number of applications it has. These applications can be broadly categorized by the method of sample insertion used. The gaseous and highly volatile liquid samples use a vacuum manifold, solids and less volatile liquids use a direct insertion probe, and complex mixtures use gas chromatography or liquid chromatography.
Vacuum manifold
In this method the sample is first inserted into a heated sample reservoir in the vacuum manifold. It then escapes into the ionization chamber through a pinhole. This method is useful with highly volatile samples that may not be compatible with other sample introduction methods.
Direct insertion EI-MS
In this method, the probe is manufactured from a long metal channel which ends in a well for holding a sample capillary. The probe is inserted into the source block through a vacuum lock. The sample is introduced to the well using a glass capillary. Next the probe is quickly heated to the desired temperature to vaporize the sample. Using this probe the sample can be positioned very close to the ionization region.
Analysis of archaeologic materials
Direct insertion electron ionization mass spectrometry (direct insertion EI-MS) has been used for the identification of archeological adhesives such as tars, resins and waxes found during excavations on archeological sites. These samples are typically investigated using gas chromatography–MS with extraction, purification, and derivatization of the samples. Due to the fact that these samples were deposited in prehistoric periods, they are often preserved in small amounts. By using direct insertion EI–MS archaeological samples, ancient organic remains like pine and pistacia resins, birch bark tar, beeswax, and plant oils as far from bronze and Iron Age periods were directly analyzed. The advantage of this technique is that the required amount of sample is less and the sample preparation is minimized.
Both direct insertion-MS and gas chromatography-MS were used and compared in a study of characterization of the organic material present as coatings in Roman and Egyptian amphoras can be taken as an example of archeological resinous materials. From this study, it reveals that, the direct insertion procedure seems to be a fast, straightforward and a unique tool which is suitable for screening of organic archeological materials which can reveal information about the major constituents within the sample. This method provides information on the degree of oxidation and the class of materials present. As a drawback of this method, less abundant components of the sample may not be identified.
Characterization of synthetic carbon clusters
Another application of direct insertion EI-MS is the characterization of novel synthetic carbon clusters isolated in the solid phase. These crystalline materials consist of C60 and C70 in the ratio of 37:1. In one investigation it has been shown that the synthetic C60 molecule is remarkably stable and that it retains its aromatic character.
Gas chromatography mass spectrometry
Gas chromatography (GC) is the most widely used method in EI-MS for sample insertion. GC can be incorporated for the separation of mixtures of thermally stable and volatile gases which are in perfect match with the electron ionization conditions.
Analysis of archaeologic materials
The GC-EI-MS has been used for the study and characterization of organic material present in coatings on Roman and Egyptian amphorae. From this analysis scientists found that the material used to waterproof the amphorae was a particular type of resin not native to the archaeological site but imported from another region. One disadvantage of this method was the long analysis time and requirement of wet chemical pre-treatment.
Environmental analysis
GC-EI-MS has been successfully used for the determination of pesticide residues in fresh food by a single injection analysis. In this analysis 81 multi-class pesticide residues were identified in vegetables. For this study the pesticides were extracted with dichloromethane and further analyzed using gas chromatography–tandem mass spectrometry (GC–MS–MS). The optimum ionization method can be identified as EI or chemical ionization (CI) for this single injection of the extract. This method is fast, simple and cost effective since high numbers of pesticides can be determined by GC with a single injection, considerably reducing the total time for the analysis.
Analysis of biological fluids
The GC-EI-MS can be incorporated for the analysis of biological fluids for several applications. One example is the determination of thirteen synthetic pyrethroid insecticide molecules and their stereoisomers in whole blood. This investigation used a new rapid and sensitive electron ionization-gas chromatography–mass spectrometry method in selective ion monitoring mode (SIM) with a single injection of the sample. All the pyrethroid residues were separated by using a GC-MS operated in electron ionization mode and quantified in selective ion monitoring mode. The detection of specific residues in blood is a difficult task due to their very low concentration since as soon as they enter the body most of the chemicals may get excreted. However, this method detected the residues of different pyrethroids down to the level 0.05–2 ng/ml. The detection of this insecticide in blood is very important since an ultra-small quantity in the body is enough to be harmful to human health, especially in children. This method is a very simple, rapid technique and therefore can be adopted without any matrix interferences. The selective ion monitoring mode provides detection sensitivity up to 0.05 ng/ml. Another application is in protein turnover studies using GC-EI-MS. This measures very low levels of d-phenylalanine which can indicate the enrichment of amino acid incorporated into tissue protein during studies of human protein synthesis. This method is very efficient since both free and protein-bound d-phenylalanine can be measured using the same mass spectrometer and only a small amount of protein is needed (about 1 mg).
Forensic applications
The GC-EI-MS is also used in forensic science. One example is the analysis of five local anesthetics in blood using headspace solid-phase microextraction (HS-SPME) and gas chromatography–mass spectrometry–electron impact ionization selected ion monitoring (GC–MS–EI-SIM). Local anesthesia is widely used but sometimes these drugs can cause medical accidents. In such cases an accurate, simple, and rapid method for the analysis of local anesthetics is required. GC-EI-MS was used in one case with an analysis time of 65 minutes and a sample size of approximately 0.2 g, a relatively small amount. Another application in forensic practice is the determination of date rape drugs (DRDs) in urine. These drugs are used to incapacitate victims and then rape or rob them. The analyses of these drugs are difficult due to the low concentrations in the body fluids and often a long time delay between the event and clinical examination. However, using GC-EI-MS allows a simple, sensitive and robust method for the identification, detection and quantification of 128 compounds of DRDs in urine.
Liquid chromatography EI-MS
Two recent approaches for coupling capillary scale liquid chromatography-electron ionization mass spectrometry (LC-EI-MS) can be incorporated for the analysis of various samples. These are capillary-scale EI-based LC/MS interface and direct-EI interface. In the capillary EI the nebulizer has been optimized for linearity and sensitivity. The direct-EI interface is a miniaturized interface for nano- and micro-HPLC in which the interfacing process takes place in a suitably modified ion source. Higher sensitivity, linearity, and reproducibility can be obtained because the elution from the column is completely transferred into the ion source. Using these two interfaces electron ionization can be successfully incorporated for the analysis of small and medium-sized molecules with various polarities. The most common applications for these interfaces in LC-MS are environmental applications such as gradient separations of the pesticides, carbaryl, propanil, and chlorpropham using a reversed phase, and pharmaceutical applications such as separation of four anti-inflammatory drugs, diphenyldramine, amitriptyline, naproxen, and ibuprofen.
Another method to categorize the applications of electron ionization is based on the separation technique which is used in mass spectroscopy. According to this category most of the time applications can be found in time of flight (TOF) or orthogonal TOF mass spectrometry (OA-TOF MS), Fourier transform ion cyclotron resonance (FT-ICR MS) and quadrupole or ion trap mass spectrometry.
Use with time-of-flight mass spectrometry
The electron ionization time of flight mass spectroscopy (EI-TOF MS) is well suited for analytical and basic chemical physics studies. EI-TOF MS is used to find ionization potentials of molecules and radicals, as well as bond dissociation energies for ions and neutral molecules. Another use of this method is to study about negative ion chemistry and physics. Autodetachment lifetimes, metastable dissociation, Rydberg electron transfer reactions and field detachment, SF6 scavenger method for detecting temporary negative ion states, and many others have all been discovered using this technique. In this method the field free ionization region allows for high precision in the electron energy and also high electron energy resolution. Measuring the electric fields down the ion flight tube determines autodetachment and metastable decomposition as well as field detachment of weakly bound negative ions.
The first description of an electron ionization orthogonal-acceleration TOF MS (EI oa-TOFMS) was in 1989. By using "orthogonal-acceleration" with the EI ion source the resolving power and sensitivity was increased. One of the key advantage of oa-TOFMS with EI sources is for deployment with gas chromatographic (GC) inlet systems, which allows chromatographic separation of volatile organic compounds to proceed at high speed.
Fourier transform ion cyclotron resonance mass spectrometry
FT- ICR EI - MS can be used for analysis of three vacuum gas oil (VGO) distillation fractions in 295-319 °C, 319-456 °C and 456-543 °C. In this method, EI at 10 eV allows soft ionization of aromatic compounds in the vacuum gas oil range. The compositional variations at the molecular level were determined from the elemental composition assignment. Ultra-high resolving power, small sample size, high reproducibility and mass accuracy (<0.4ppm) are the special features in this method. The major product was aromatic hydrocarbons in all three samples. In addition, many sulfur-, nitrogen-, and oxygen-containing compounds were directly observed when the concentration of this heteroatomic species increased with the boiling point. Using data analysis it gave the information about compound types (rings plus double bonds), their carbon number distributions for hydrocarbon and heteroatomic compounds in the distillation fractions, increasing average molecular weight (or carbon number distribution) and aromaticity with increasing boiling temperature of the petroleum fractions.
Ion trap mass spectrometry
Ion trap EI MS can be incorporated for the identification and quantitation of nonylphenol polyethoxylate (NPEO) residues and their degradation products such as nonylphenol polyethoxy carboxylates and carboxyalkylphenol ethoxy carboxylates, in the samples of river water and sewage effluent. Form this research, they have found out that the ion trap GC- MS is a reliable and convenient analytical approach with variety of ionization methods including EI, for the determination of target compounds in environmental samples.
Advantages and disadvantages
There are several advantages and also disadvantages by using EI as the ionization method in mass spectrometry. These are listed below.
See also
Ion source
Penning ionization
Chemical ionization
Spark ionization
Thermal ionization
References
Notes
External links
NIST Chemistry WebBook
Mass Spectrometry. Michigan State University.
Ion source
Mass spectrometry
Scientific techniques | Electron ionization | [
"Physics",
"Chemistry"
] | 4,051 | [
"Spectrum (physical sciences)",
"Instrumental analysis",
"Mass",
"Ion source",
"Mass spectrometry",
"Matter"
] |
340,291 | https://en.wikipedia.org/wiki/Stick%20shaker | A stick shaker is a mechanical device designed to rapidly and noisily vibrate the control yoke (the "stick") of an aircraft, warning the flight crew that an imminent aerodynamic stall has been detected. It is typically present on the majority of large civil jet aircraft, as well as most large military planes.
The stick shaker comprises a key component of an aircraft's stall protection system. Accidents, such as the 1963 BAC One-Eleven test crash, were attributable to aerodynamic stalls and motivated aviation regulatory bodies to establish requirements for certain aircraft to be outfitted with stall protection measures, such as the stick shaker and stick pusher, to reduce such occurrences. While the stick shaker has become relatively prevalent amongst airliners and large transport aircraft, such devices are not infallible and require flight crews to be appropriately trained on their functionality and how to respond to their activation. Several instances of aircraft entering stalls have occurred even with properly functioning stick shakers, largely due to pilots reacting improperly.
History
When many small aircraft approach the critical angle of attack that will result in an aerodynamic stall, the smooth flow of air over the wings is interrupted, causing turbulent airflow at the trailing edge of the wings. Depending on the aircraft size or design, that turbulent air, known as buffet, typically impacts the elevator at the rear end of the aircraft, and that in turn causes vibrations that are transmitted through control cables and can be felt by the pilot on the yoke as violent shaking. This natural shaking of the control yoke serves as an early warning to pilots that a stall is developing.
For very large aircraft, fly-by-wire aircraft and some aircraft with complex tail designs, there is no buffet effect on the control yoke, because the turbulent air does not reach the elevator, or because any movement in the elevator from buffet is not transmitted back to the control yoke. This deprives pilots of these aircraft of one of the important early warnings that they are about to enter a stall.
Boeing aircraft designers were the first to solve this problem by creating a mechanical device, which they named a stick shaker, that shakes the control yoke in a similar way to how a yoke is shaken naturally in smaller aircraft as the aircraft approaches its critical angle of attack.
Stick shakers were being developed as early as 1949.
During 1963, a BAC One-Eleven airliner was lost after having crashed during a stall test. The pilots pushed the T-tailed plane past the limits of stall recovery and entered a deep stall state, in which the disturbed air from the stalled wing had rendered the elevator ineffective, directly leading to a loss of control and crash. As a consequence of the crash, a combined stick shaker/pusher system was installed in all production BAC One-Eleven airliners. A wider consequence of the incident was the instatement of a new requirement related to the pilot's ability to identify and overcome stall conditions; a design of transport category aircraft that fails to comply with the specifics of this requirement may be acceptable if the aircraft is equipped with a stick pusher.
Following the crash of American Airlines Flight 191 on 25 May 1979, the Federal Aviation Administration (FAA) issued an airworthiness directive, which mandated the installation and operation of stick shakers on both sets of flight controls on most models of the McDonnell Douglas DC-10, a trijet airliner. (Previously, only the captain's controls were equipped with a stick shaker on the DC-10; in the case of Flight 191, this single stick shaker had been disabled by a partial electrical power failure early in the accident sequence.) In addition to regulatory pressure, various aircraft manufacturers have endeavoured to devise their own improved stall protection systems, many of which have included the stick shaker. The American aerospace company Boeing had designed and integrated stall warning systems into numerous aircraft that it has produced.
A wide range of aircraft have incorporated stick shakers into their cockpits. Textron Aviation's Citation Longitude business jet is one such example, as is the Pilatus PC-24 light business jet, and Bombardier Aviation's Challenger 600 family of business jets. Commercial airliners such as the newer models of the Boeing 737, the Boeing 767, and the Embraer E-Jet E2 family have also included stick shakers in the aircraft's stall protection systems.
Function in stall protection systems
The stick shaker is a major element of an aircraft's stall protection system. The system is composed of fuselage or wing-mounted angle of attack (AOA) sensors that are connected to an avionics computer, which receives inputs from the AOA sensors along with a variety of other flight systems. When this data indicates an imminent stall condition, the computer actuates both the stick shaker and an auditory alert. The shaker itself is composed of an electric motor connected to a deliberately unbalanced flywheel. When actuated, the shaker induces a forceful, noisy, and entirely unmistakable shaking of the control yoke. This shaking of the control yoke matches the frequency and amplitude of the stick shaking that occurs due to airflow separation in low-speed aircraft as they approach the stall. The stick shaking is intended to act as a backup to the auditory stall alert, in cases where the flight crew may be distracted.
Stick pusher
Other stall protection systems include the stick pusher, a device that automatically pushes forward on the control yoke, commanding a reduction in the aircraft's angle of attack and thus preventing the aircraft from entering a full stall. In the majority of circumstances, the stick pusher will not activate until shortly after the stick shaker has given its warning of near-stall conditions being detected, and will not activate if the flight crew have performed appropriate actions to reduce the likelihood of stalling by lowering the angle of attack. Under most regulatory regimes, an aircraft's stall protection systems must be tested and armed prior to takeoff, as well as remain armed throughout the flight; for this reason, startup checklists normally include performing such tests as a matter of routine.
Audio
The vibration of the stick shaker is loud enough that it can be commonly heard on cockpit voice recorder (CVR) recordings of aircraft that have encountered stall conditions. This level of vigorous movement is intentional, the stick shaker having been designed to be impossible to ignore. To unfamiliar flight crews, the stall warning system can be viewed as aggressive and impatient, hence why it has become commonplace for the system to be introduced to trainee pilots via a flight simulator rather than a live aircraft. To fly without them would increase the likelihood of the aircraft encountering, and improperly responding to, a stall event.
Flight crew factor
During the 2000s, there was a series of accidents that were attributed, at least in part, to their flight crews having made improper responses to the activation of the stall warning systems. During the early 2010s, in response to this wave of accidents, the FAA issued guidance urging operators to ensure that flight crews are properly training on the correct use of these aids.
See also
1963 BAC One-Eleven test crash
Dual control (aviation)
References
External links
FAA Advisory Circular 120-109, Stall and Stick Pusher Training
Manual on Aeroplane Upset Prevention and Recovery Training via icao.int
Aircraft controls
Mechanical vibrations | Stick shaker | [
"Physics",
"Engineering"
] | 1,483 | [
"Structural engineering",
"Mechanics",
"Mechanical vibrations"
] |
340,294 | https://en.wikipedia.org/wiki/Pentagonal%20number%20theorem | In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that
In other words,
The exponents 1, 2, 5, 7, 12, ... on the right hand side are given by the formula for k = 1, −1, 2, −2, 3, ... and are called (generalized) pentagonal numbers . (The constant term 1 corresponds to .)
This holds as an identity of convergent power series for , and also as an identity of formal power series.
A striking feature of this formula is the amount of cancellation in the expansion of the product.
Relation with partitions
The identity implies a recurrence for calculating , the number of partitions of n:
or more formally,
where the summation is over all nonzero integers k (positive and negative) and is the kth generalized pentagonal number. Since for all , the apparently infinite series on the right has only finitely many non-zero terms, enabling an efficient calculation of p(n).
Franklin's bijective proof
The theorem can be interpreted combinatorially in terms of partitions. In particular, the left hand side is a generating function for the number of partitions of n into an even number of distinct parts minus the number of partitions of n into an odd number of distinct parts. Each partition of n into an even number of distinct parts contributes +1 to the coefficient of xn; each partition into an odd number of distinct parts contributes −1. (The article on unrestricted partition functions discusses this type of generating function.)
For example, the coefficient of x5 is +1 because there are two ways to split 5 into an even number of distinct parts (4 + 1 and 3 + 2), but only one way to do so for an odd number of distinct parts (the one-part partition 5). However, the coefficient of x12 is −1 because there are seven ways to partition 12 into an even number of distinct parts, but there are eight ways to partition 12 into an odd number of distinct parts, and 7 − 8 = −1.
This interpretation leads to a proof of the identity by canceling pairs of matched terms (involution method). Consider the Ferrers diagram of any partition of n into distinct parts. For example, the diagram below shows n = 20 and the partition 20 = 7 + 6 + 4 + 3.
Let m be the number of elements in the smallest row of the diagram (m = 3 in the above example). Let s be the number of elements in the rightmost 45 degree line of the diagram (s = 2 dots in red above, since 7 − 1 = 6, but 6 − 1 > 4). If m > s, take the rightmost 45-degree line and move it to form a new row, as in the matching diagram below.
If m ≤ s (as in our newly formed diagram where m = 2, s = 5) we may reverse the process by moving the bottom row to form a new 45 degree line (adding 1 element to each of the first m rows), taking us back to the first diagram.
A bit of thought shows that this process always changes the parity of the number of rows, and applying the process twice brings us back to the original diagram. This enables us to pair off Ferrers diagrams contributing 1 and −1 to the xn term of the series, resulting in a net coefficient of 0 for xn. This holds for every term except when the process cannot be performed on every Ferrers diagram with n dots. There are two such cases:
1) m = s and the rightmost diagonal and bottom row meet. For example,
Attempting to perform the operation would lead us to:
which fails to change the parity of the number of rows, and is not reversible in the sense that performing the operation again does not take us back to the original diagram. If there are m elements in the last row of the original diagram, then
where the new index k is taken to equal m. Note that the sign associated with this partition is (−1)s, which by construction equals (−1)m and (−1)k.
2) m = s + 1 and the rightmost diagonal and bottom row meet. For example,
Our operation requires us to move the right diagonal to the bottom row, but that would lead to two rows of three elements, forbidden since we're counting partitions into distinct parts. This is the previous case but with one fewer row, so
where we take k = 1−m (a negative integer). Here the associated sign is (−1)s with s = m − 1 = −k, therefore the sign is again (−1)k.
In summary, it has been shown that partitions into an even number of distinct parts and an odd number of distinct parts exactly cancel each other, producing null terms 0xn, except if n is a generalized pentagonal number , in which case there is exactly one Ferrers diagram left over, producing a term (−1)kxn. But this is precisely what the right side of the identity says should happen, so we are finished.
Partition recurrence
We can rephrase the above proof, using integer partitions, which we denote as:
,
where .
The number of partitions of n is the partition function p(n) having generating function:
Note that is the reciprocal of the product on the left hand side of our identity:
Let us denote the expansion of our product by
so that
Multiplying out the left hand side and equating coefficients on the two sides, we obtain
a0 p(0) = 1 and for all . This gives a recurrence relation defining p(n) in terms of an, and vice versa a recurrence for an in terms of p(n). Thus, our desired result:
for is equivalent to the identity where and i ranges over all integers such that (this range includes both positive and negative i, so as to use both kinds of generalized pentagonal numbers). This in turn means:
In terms of sets of partitions, this is equivalent to saying that the following sets are of equal cardinality:
and
where denotes the set of all partitions of .
All that remains is to give a bijection from one set to the other, which is accomplished by the function φ from X to Y which maps the partition to the partition defined by:
This is an involution (a self-inverse mapping), and thus in particular a bijection, which proves our claim and the identity.
See also
The pentagonal number theorem occurs as a special case of the Jacobi triple product.
Q-series generalize Euler's function, which is closely related to the Dedekind eta function, and occurs in the study of modular forms. The modulus of the Euler function (see there for picture) shows the fractal modular group symmetry and occurs in the study of the interior of the Mandelbrot set.
References
External links
On Euler's Pentagonal Theorem at MathPages
De mirabilis proprietatibus numerorum pentagonalium at Scholarly Commons.
Theorems in number theory
Articles containing proofs
Integer partitions | Pentagonal number theorem | [
"Mathematics"
] | 1,501 | [
"Articles containing proofs",
"Theorems in number theory",
"Integer partitions",
"Mathematical problems",
"Mathematical theorems",
"Number theory"
] |
340,302 | https://en.wikipedia.org/wiki/Slow%20flight | In aviation, slow flight is the region of flight below the maximum lift to drag ratio, where induced drag becomes more significant than parasitic drag. Slow flight can be as slow as 3-5 knots above stall airspeed.
Slow flight is sometimes referred to as the “region of reversed command” or the “back side of the power curve”. This is because in slow flight, more power is required to maintain straight and level flight at lower airspeeds. A very high angle of attack is required to maintain altitude in slow flight.
At these low airspeeds, flight control surfaces begin to lose their effectiveness due to the reduction in airflow over them. Ailerons are the most affected, and roll control is significantly degraded. If ailerons are used in slow flight, there is a possibility that the high wing will stall due to the increased angle of attack, sending the aircraft into a spin. In many modern aircraft, flight envelope protection in the aircraft flight control system prevents this from happening. The rudder remains effective in slow flight, and yaw provided by it can be used to control the bank angle and direction of the aircraft.
References
Aerodynamics | Slow flight | [
"Chemistry",
"Engineering"
] | 234 | [
"Aerospace engineering",
"Aerodynamics",
"Fluid dynamics"
] |
340,356 | https://en.wikipedia.org/wiki/Sodium%20stearoyl%20lactylate | Sodium stearoyl-2-lactylate (sodium stearoyl lactylate or SSL) is a versatile, FDA approved food additive used to improve the mix tolerance and volume of processed foods. It is one type of a commercially available lactylate. SSL is non-toxic, biodegradable, and typically manufactured using biorenewable feedstocks. Because SSL is a safe and highly effective food additive, it is used in a wide variety of products ranging from baked goods and desserts to pet foods.
As described by the Food Chemicals Codex 7th edition, SSL is a cream-colored powder or brittle solid. SSL is currently manufactured by the esterification of stearic acid with lactic acid and partially neutralized with either food-grade soda ash (sodium carbonate) or caustic soda (concentrated sodium hydroxide). Commercial grade SSL is a mixture of sodium salts of stearoyl lactylic acids and minor proportions of other sodium salts of related acids. The HLB for SSL is 10–12. SSL is slightly hygroscopic, soluble in ethanol and in hot oil or fat, and dispersible in warm water. These properties are the reason that SSL is an excellent emulsifier for fat-in-water emulsions and can also function as a humectant.
Food labeling requirements
To be labeled as SSL for sale within the United States, the product must conform to the specifications detailed in 21 CFR 172.846 and the “Food Chemicals Codex,” 3d Ed. (1981), pp. 300-301. In the EU, the product must conform to the specifications detailed in Regulation (EC) No 96/77. For the 7th edition of the FCC and Regulation (EC) No 96/77, these specifications are:
To be labeled as SSL for sale in other regions, the product must conform to the specifications detailed in that region's codex.
Food applications and maximum use levels
SSL finds widespread application in baked goods, pancakes, waffles, cereals, pastas, instant rice, desserts, icings, fillings, puddings, toppings, sugar confectionaries, powdered beverage mixes, creamers, cream liqueurs, dehydrated potatoes, snack dips, sauces, gravies, chewing gum, dietetic foods, minced and diced canned meats, mostarda di frutta, and pet food. Approved uses and maximum use levels in the United States are described in 21 CFR 172.846 and 21 CFR 177.120. In the European Union, the approved uses and maximum use levels are described in Regulation (EC) No 95/2.
The largest marketed use of SSL is in yeast-raised bakery products. SSL is used in the majority of manufactured breads, buns, wraps, tortillas, and similar bread-based products to ensure consistent product quality. Use levels for baked goods will vary between 0.25 - 0.5% based on flour. The typical application level is 0.375% and will be adjusted depending on the type and quality of flour used.
Compared to calcium stearoyl-2-lactylate (CSL), SSL offers some advantages. First, SSL disperses and hydrates more readily in water than CSL. Therefore, SSL does not require pre-hydration. Second, SSL provides better crumb softening than CSL. SSL's crumb softening effect is noticeable up to 5–7 days after baking. Third, in rich bread formulations (e.g. pan bread and hamburger buns), SSL provides better dough strengthening than CSL. Use of SSL in these formulations will yield (nearly) perfect symmetry in the finished baked good. Because of these characteristics, SSL is currently used in more baking applications than CSL.
Research has explored the possibility of replacing SSL with the use of enzymes. Enzyme technologies, by themselves, have not been able to completely replace SSL. A major limitation of enzymes is the production of gummy bread of unpredictable quality. Also, enzymes often do not augment dough strength, which is necessary to prevent loaf collapse during baking. Currently, enzymes are being used in conjunction with SSL to maximize the shelf life of bread. SSL is very good at increasing softness of bread during the first week after baking. Enzyme technology works best after the first five days of shelf life. Therefore, bread with optimal softness throughout the desired shelf life is obtained by using a combination of these technologies.
Health and safety
Lactylates, including SSL, have been subjected to extensive safety evaluations prior to being FDA approved for use as a food additive. The oral LD50 of SSL for rats was established by Schuler and Thornton in 1952 as being over 25 g/kg body weight. In 2010, Lamb established the no-observed-adverse-effect level of SSL at 5% of the total diet and recommended an acceptable daily intake of 22.1 mg/kg bw/day for human consumption.
References
Organic sodium salts
Food additives
E-number additives | Sodium stearoyl lactylate | [
"Chemistry"
] | 1,066 | [
"Organic sodium salts",
"Salts"
] |
340,363 | https://en.wikipedia.org/wiki/Economic%20statistics | Economic statistics is a topic in applied statistics and applied economics that concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is closely related to business statistics and econometrics. It is also common to call the data themselves "economic statistics", but for this usage, "economic data" is the more common term.
Overview
The data of concern to economic statistics may include those of an economy within a region, country, or group of countries. Economic statistics may also refer to a subtopic of official statistics for data produced by official organizations (e.g. national statistical services, intergovernmental organizations such as United Nations, European Union or OECD, central banks, and ministries).
Analyses within economic statistics both make use of and provide the empirical data needed in economic research, whether descriptive or econometric. They are a key input for decision making as to economic policy. The subject includes statistical analysis of topics and problems in microeconomics, macroeconomics, business, finance, forecasting, data quality, and policy evaluation. It also includes such considerations as what data to collect in order to quantify some particular aspect of an economy and of how best to collect in any given instance.
See also
Business statistics
Econometrics
Survey of production
References
Citations
Sources
Allen, R. G. D., 1956. "Official Economic Statistics," Economica, N.S., 23(92), pp. 360-365.
Crum, W. L., 1925. An Introduction to the Methods of Economic Statistics, AW Shaw Co.
Giovanini, Enrico, 2008. Understanding Economic Statistics. OECD Publishing.
Fox, Karl A., 1968. Intermediate Economic Statistics, Wiley. Description.
Kane, Edward J., 1968. Economic Statistics and Econometrics, Harper and Row.
Morgenstern, Oskar, [1950] 1963. On the Accuracy of Economic Observations. 2nd rev. ed. ("The Accuracy of Economic Observation" ch. 16). Princeton University Press.
Mirer, Thad W., 1995. Economic Statistics and Econometrics, 3rd ed. Prentice Hall. Description.
Persons, Warren M., 1910. "The Correlation of Economic Statistics," Publications of the American Statistical Association, 12(92), pp. 287-322.
Wonnacott, Thomas H., and Ronald J. Wonnacott, 1990. Introductory Statistics for Business and Economics, 4th ed., Wiley.
Ullah, Aman, and David E. A. Giles, ed., 1998. Handbook of Applied Economic Statistics, Marcel Dekker. Description, preview, and back cover.
Zellner, Arnold, ed. 1968. Readings in Economic Statistics and Econometrics, Little, Brown & Co.
Journals
Journal of Business and Economic Statistics
Review of Economics and Statistics (from Review of Economic Statistics, 1919–47)
External links
Economic statistics section United Nations Economic Commission for Europe
Statistics from UCB Libraries GovPubs
Economic statistics: The White House pages on U.S. economic statistics
Historical Financial Statistics: Center for Financial Stability (emphasizes statistics before about 1950)
Fundamental principles of official statistics: United Nations, Statistics Division
Economic statistics (papers from methodological meetings): UNECE
OANDA FXEconostats: Historical graphical economic data of major industrial countries
OECD Official Statistics Organisation for Economic Cooperation and Development (OECD) Statistics
Eurostat: The European Commission's Statistical Office
Applied statistics
Mathematical and quantitative methods (economics)
Socio-economic statistics | Economic statistics | [
"Mathematics"
] | 722 | [
"Applied mathematics",
"Applied statistics"
] |
340,440 | https://en.wikipedia.org/wiki/Fluid%20mosaic%20model | The fluid mosaic model explains various characteristics regarding the structure of functional cell membranes. According to this biological model, there is a lipid bilayer (two molecules thick layer consisting primarily of amphipathic phospholipids) in which protein molecules are embedded. The phospholipid bilayer gives fluidity and elasticity to the membrane. Small amounts of carbohydrates are also found in the cell membrane. The biological model, which was devised by Seymour Jonathan Singer and Garth L. Nicolson in 1972, describes the cell membrane as a two-dimensional liquid where embedded proteins are generally randomly distributed. For example, it is stated that "A prediction of the fluid mosaic model is that the two-dimensional long-range distribution of any integral protein in the plane of the membrane is essentially random."
Chemical makeup
Experimental evidence
The fluid property of functional biological membranes had been determined through labeling experiments, x-ray diffraction, and calorimetry. These studies showed that integral membrane proteins diffuse at rates affected by the viscosity of the lipid bilayer in which they were embedded, and demonstrated that the molecules within the cell membrane are dynamic rather than static.
Previous models of biological membranes included the Robertson Unit Membrane Model and the Davson-Danielli Tri-Layer model. These models had proteins present as sheets neighboring a lipid layer, rather than incorporated into the phospholipid bilayer. Other models described repeating, regular units of protein and lipid. These models were not well supported by microscopy and thermodynamic data, and did not accommodate evidence for dynamic membrane properties.
An important experiment that provided evidence supporting fluid and dynamic biological was performed by Frye and Edidin. They used Sendai virus to force human and mouse cells to fuse and form a heterokaryon. Using antibody staining, they were able to show that the mouse and human proteins remained segregated to separate halves of the heterokaryon a short time after cell fusion. However, the proteins eventually diffused and over time the border between the two halves was lost. Lowering the temperature slowed the rate of this diffusion by causing the membrane phospholipids to transition from a fluid to a gel phase. Singer and Nicolson rationalized the results of these experiments using their fluid mosaic model.
The fluid mosaic model explains changes in structure and behavior of cell membranes under different temperatures, as well as the association of membrane proteins with the membranes. While Singer and Nicolson had substantial evidence drawn from multiple subfields to support their model, recent advances in fluorescence microscopy and structural biology have validated the fluid mosaic nature of cell membranes.
Subsequent developments
Membrane asymmetry
Additionally, the two leaflets of biological membranes are asymmetric and divided into subdomains composed of specific proteins or lipids, allowing spatial segregation of biological processes associated with membranes. Cholesterol and cholesterol-interacting proteins can concentrate into lipid rafts and constrain cell signaling processes to only these rafts. Another form of asymmetry was shown by the work of Mouritsen and Bloom in 1984, where they proposed a Mattress Model of lipid-protein interactions to address the biophysical evidence that the membrane can range in thickness and hydrophobicity of proteins.
Non-bilayer membranes
The existence of non-bilayer lipid formations with important biological functions was confirmed subsequent to publication of the fluid mosaic model. These membrane structures may be useful when the cell needs to propagate a non bilayer form, which occurs during cell division and the formation of a gap junction.
Membrane curvature
The membrane bilayer is not always flat. Local curvature of the membrane can be caused by the asymmetry and non-bilayer organization of lipids as discussed above. More dramatic and functional curvature is achieved through BAR domains, which bind to phosphatidylinositol on the membrane surface, assisting in vesicle formation, organelle formation and cell division. Curvature development is in constant flux and contributes to the dynamic nature of biological membranes.
Lipid movement within the membrane
During the 1970s, it was acknowledged that individual lipid molecules undergo free lateral diffusion within each of the layers of the lipid membrane. Diffusion occurs at a high speed, with an average lipid molecule diffusing ~2μm, approximately the length of a large bacterial cell, in about 1 second. It has also been observed that individual lipid molecules rotate rapidly around their own axis. Moreover, phospholipid molecules can, although they seldom do, migrate from one side of the lipid bilayer to the other (a process known as flip-flop). However, flip-flop movement is enhanced by flippase enzymes. The processes described above influence the disordered nature of lipid molecules and interacting proteins in the lipid membranes, with consequences to membrane fluidity, signaling, trafficking and function.
Restrictions to lateral diffusion
There are restrictions to the lateral mobility of the lipid and protein components in the fluid membrane imposed by zonation. Early attempts to explain the assembly of membrane zones include the formation of lipid rafts and “cytoskeletal fences”, corrals wherein lipid and membrane proteins can diffuse freely, but that they can seldom leave. These ideas remain controversial, and alternative explanations are available such as the proteolipid code.
Lipid rafts
Lipid rafts are membrane nanometric platforms with a particular lipid and protein composition that laterally diffuse, navigating on the liquid bilipid layer. Sphingolipids and cholesterol are important building blocks of the lipid rafts.
Protein complexes
Cell membrane proteins and glycoproteins do not exist as single elements of the lipid membrane, as first proposed by Singer and Nicolson in 1972. Rather, they occur as diffusing complexes within the membrane. The assembly of single molecules into these macromolecular complexes has important functional consequences for the cell; such as ion and metabolite transport, signaling, cell adhesion, and migration.
Cytoskeletal fences (corrals) and binding to the extracellular matrix
Some proteins embedded in the bilipid layer interact with the extracellular matrix outside the cell, cytoskeleton filaments inside the cell, and septin ring-like structures. These interactions have a strong influence on shape and structure, as well as on compartmentalization. Moreover, they impose physical constraints that restrict the free lateral diffusion of proteins and at least some lipids within the bilipid layer.
When integral proteins of the lipid bilayer are tethered to the extracellular matrix, they are unable to diffuse freely. Proteins with a long intracellular domain may collide with a fence formed by cytoskeleton filaments. Both processes restrict the diffusion of proteins and lipids directly involved, as well as of other interacting components of the cell membranes.
Septins are a family of GTP-binding proteins highly conserved among eukaryotes. Prokaryotes have similar proteins called paraseptins. They form compartmentalizing ring-like structures strongly associated with the cell membranes. Septins are involved in the formation of structures such as, cilia and flagella, dendritic spines, and yeast buds.
Historical timeline
1895 – Ernest Overton hypothesized that cell membranes are made out of lipids.
1925 – Evert Gorter and François Grendel found that red blood cell membranes are formed by a fatty layer two molecules thick, i.e. they described the bilipid nature of the cell membrane.
1935 – Hugh Davson and James Danielli proposed that lipid membranes are layers composed by proteins and lipids with pore-like structures that allow specific permeability for certain molecules. Then, they suggested a model for the cell membrane, consisting of a lipid layer surrounded by protein layers at both sides of it.
1957 – J. David Robertson, based on electron microscopy studies, establishes the "Unit Membrane Hypothesis". This, states that all membranes in the cell, i.e. plasma and organelle membranes, have the same structure: a bilayer of phospholipids with monolayers of proteins at both sides of it.
1972 – SJ Singer and GL Nicolson proposed the fluid mosaic model as an explanation for the data and latest evidence regarding the structure and thermodynamics of cell membranes.
1997 – K Simons and E Ikonen proposed the lipid raft theory as an initial explanation of membrane zonation.
2024 – TA Kervin and M Overduin proposed the proteolipid code to fully explain membrane zonation as the lipid raft theory became increasingly controversial.
Notes and references
Membrane biology
Organelles
Cell anatomy | Fluid mosaic model | [
"Chemistry"
] | 1,788 | [
"Membrane biology",
"Molecular biology"
] |
340,476 | https://en.wikipedia.org/wiki/Serial%20Peripheral%20Interface | Serial Peripheral Interface (SPI) is a de facto standard (with many variants) for synchronous serial communication, used primarily in embedded systems for short-distance wired communication between integrated circuits.
SPI follows a master–slave architecture, called main–sub herein, where one main device orchestrates communication with one or more sub (peripheral) devices by driving the clock and chip select signals.
Motorola's original specification (from the early 1980s) uses four logic signals, aka lines or wires, to support full duplex communication. It is sometimes called a four-wire serial bus to contrast with three-wire variants which are half duplex, and with the two-wire I²C and 1-Wire serial buses.
Typical applications include interfacing microcontrollers with peripheral chips for Secure Digital cards, liquid crystal displays, analog-to-digital and digital-to-analog converters, flash and EEPROM memory, and various communication chips.
Although SPI is a synchronous serial interface, it is different from Synchronous Serial Interface (SSI). SSI employs differential signaling and provides only a single simplex communication channel.
Operation
Commonly, SPI has four logic signals. Variations may use different names or have different signals. Historical terms are shown in parentheses.
{| class="wikitable"
! Abbr.!! Name !! Description
|-
| || || Active-low chip select signal from main toenable communication with a specific sub device
|-
| || || Clock signal from main
|-
| || || Serial data from main, most-significant bit first
|-
| || || Serial data from sub, most-significant bit first
|}
MOSI on a main outputs to MOSI on a sub. MISO on a sub outputs to MISO on a main.
Each device internally uses a shift register for serial communication, which together forms an inter-chip circular buffer.
Sub devices should use tri-state outputs so their MISO signal becomes high impedance (electrically disconnected) when the device is not selected. Subs without tri-state outputs cannot share a MISO line with other subs without using an external tri-state buffer.
Data transmission
To begin communication, the SPI main first selects a sub device by pulling its low. (Note: the bar above indicates it is an active low signal, so a low voltage means "selected", while a high voltage means "not selected")
If a waiting period is required, such as for an analog-to-digital conversion, the main must wait for at least that period of time before issuing clock cycles.
During each SPI clock cycle, full-duplex transmission of a single bit occurs. The main sends a bit on the MOSI line while the sub sends a bit on the MISO line, and then each reads their corresponding incoming bit. This sequence is maintained even when only one-directional data transfer is intended.
Transmission using a single sub (Figure 1) involves one shift register in the main and one shift register in the sub, both of some given word size (e.g. 8 bits), connected in a virtual ring topology. Data is usually shifted out with the most-significant bit (MSB) first. On the clock edge, both main and sub shift out a bit to its counterpart. On the next clock edge, each receiver samples the transmitted bit and stores it in the shift register as the new least-significant bit. After all bits have been shifted out and in, the main and sub have exchanged register values. If more data needs to be exchanged, the shift registers are reloaded and the process repeats. Transmission may continue for any number of clock cycles. When complete, the main stops toggling the clock signal, and typically deselects the sub.
If a single sub device is used, its pin may be fixed to logic low if the sub permits it. With multiple sub devices, a multidrop configuration requires an independent signal from the main for each sub device, while a daisy-chain configuration only requires one signal.
Every sub on the bus that has not been selected should disregard the input clock and MOSI signals. And to prevent contention on MISO, non-selected subs must use tristate output. Subs that aren't already tristate will need external tristate buffers to ensure this.
Clock polarity and phase
In addition to setting the clock frequency, the main must also configure the clock polarity and phase with respect to the data. Motorola named these two options as CPOL and CPHA (for clock polarity and clock phase) respectively, a convention most vendors have also adopted.
The SPI timing diagram shown is further described below:
CPOL represents the polarity of the clock. Polarities can be converted with a simple inverter.
SCLK is a clock which idles at the logical low voltage.
SCLK is a clock which idles at the logical high voltage.
CPHA represents the phase of each data bit's transmission cycle relative to SCLK.
For CPHA=0:
The first data bit is output immediately when activates.
Subsequent bits are output when SCLK transitions to its idle voltage level.
Sampling occurs when SCLK transitions from its idle voltage level.
For CPHA=1:
The first data bit is output on SCLK's first clock edge after activates.
Subsequent bits are output when SCLK transitions from its idle voltage level.
Sampling occurs when SCLK transitions to its idle voltage level.
Conversion between these two phases is non-trivial.
Note: MOSI and MISO signals are usually stable (at their reception points) for the half cycle until the next bit's transmission cycle starts, so SPI main and sub devices may sample data at different points in that half cycle, for flexibility, despite the original specification.
Mode numbers
The combinations of polarity and phases are referred to by these "SPI mode" numbers with CPOL as the high order bit and CPHA as the low order bit:
Notes:
Another commonly used notation represents the mode as a (CPOL, CPHA) tuple; e.g., the value '(0, 1)' would indicate CPOL=0 and CPHA=1.
In Full Duplex operation, the main device could transmit and receive with different modes. For instance, it could transmit in Mode 0 and be receiving in Mode 1 at the same time.
Different vendors may use different naming schemes, like CKE for clock edge or NCPHA for the inversion of CPHA.
Valid communications
Some sub devices are designed to ignore any SPI communications in which the number of clock pulses is greater than specified. Others do not care, ignoring extra inputs and continuing to shift the same output bit. It is common for different devices to use SPI communications with different lengths, as, for example, when SPI is used to access an IC's scan chain by issuing a command word of one size (perhaps 32 bits) and then getting a response of a different size (perhaps 153 bits, one for each pin in that scan chain).
Interrupts
Interrupts are outside the scope of SPI; their usage is neither forbidden nor specified, and so may optionally be implemented.
From main to sub
Microcontrollers configured as sub devices may have hardware support for generating interrupt signals to themselves when data words are received or overflow occurs in a receive FIFO buffer, and may also set up an interrupt routine when their chip select input line is pulled low or high.
From sub to main
SPI subs sometimes use an out-of-band signal (another wire) to send an interrupt signal to a main. Examples include pen-down interrupts from touchscreen sensors, thermal limit alerts from temperature sensors, alarms issued by real-time clock chips, SDIO and audio jack insertions for an audio codec. Interrupts to main may also be faked by using polling (similarly to USB 1.1 and 2.0).
Software design
SPI lends itself to a "bus driver" software design. Software for attached devices is written to call a "bus driver" that handles the actual low-level SPI hardware. This permits the driver code for attached devices to port easily to other hardware or a bit-banging software implementation.
Bit-banging the protocol
The pseudocode below outlines a software implementation ("bit-banging") of SPI's protocol as a main with simultaneous output and input. This pseudocode is for CPHA=0 and CPOL=0, thus SCLK is pulled low before is activated and bits are inputted on SCLK's rising edge while bits are outputted on SCLK's falling edge.
Initialize SCLK as low and as high
Pull low to select the sub
Loop for however many number of bytes to transfer:
Initializewith the next output byte to transmit
Loop 8 times:
Left-Shift the next output bit fromto MOSI
NOP for the sub's setup time
Pull SCLK high
Left-Shift the next input bit from MISO into
NOP for the sub's hold time
Pull SCLK low
now contains that recently-received byte and can be used as desired
Pull high to unselect the sub
Bit-banging a sub's protocol is similar but different from above. An implementation might involve busy waiting for to fall or triggering an interrupt routine when falls, and then shifting in and out bits when the received SCLK changes appropriately for however long the transfer size is.
Bus topologies
Though the previous operation section focused on a basic interface with a single sub, SPI can instead communicate with multiple subs using multidrop, daisy chain, or expander configurations.
Multidrop configuration
In the multidrop bus configuration, each sub has its own , and the main selects only one at a time. MISO, SCLK, and MOSI are each shared by all devices. This is the way SPI is normally used.
Since the MISO pins of the subs are connected together, they are required to be tri-state pins (high, low or high-impedance), where the high-impedance output must be applied when the sub is not selected. Sub devices not supporting tri-state may be used in multidrop configuration by adding a tri-state buffer chip controlled by its signal. (Since only a single signal line needs to be tristated per sub, one typical standard logic chip that contains four tristate buffers with independent gate inputs can be used to interface up to four sub devices to an SPI bus)Caveat: All signals should start high (to indicate no chips are selected) before sending initialization messages to any sub, so other uninitialized subs ignore messages not addressed to them. This is a concern if the main uses general-purpose input/output (GPIO) pins (which may default to an undefined state) for and if the main uses separate software libraries to initialize each device. One solution is to configure all GPIOs used for to output a high voltage for all subs before running initialization code from any of those software libraries. Another solution is to add a pull-up resistor on each , to ensure that all signals are initially high.
Daisy chain configuration
Some products that implement SPI may be connected in a daisy chain configuration, where the first sub's output is connected to the second sub's input, and so on with subsequent subs, until the final sub, whose output is connected back to the main's input. This effectively merges the individual communication shift registers of each sub to form a single larger combined shift register that shifts data through the chain. This configuration only requires a single line from the main, rather than a separate line for each sub.
In addition to using SPI-specific subs, daisy-chained SPI can include discrete shift registers for more pins of inputs (e.g. using the parallel-in serial-out 74xx165) or outputs (e.g. using the serial-in parallel-out 74xx595) chained indefinitely. Other applications that can potentially interoperate with daisy-chained SPI include SGPIO, JTAG, and I2C.
Expander configurations
Expander configurations use SPI-controlled addressing units (e.g. binary decoders, demultiplexers, or shift registers) to add chip selects.
For example, one can be used for transmitting to a SPI-controlled demultiplexer an index number controlling its select signals, while another is routed through that demultiplexer according to that index to select the desired sub.
Pros and cons
Advantages
Full duplex communication in the default version of this protocol
Push-pull drivers (as opposed to open drain) provide relatively good signal integrity and high speed
Higher throughput than I²C or SMBus
SPI's protocol has no maximum clock speed, however:
Individual devices specify acceptable clock frequencies
Wiring and electronics limit frequency
Complete protocol flexibility for the bits transferred
Not limited to 8-bit symbols
Arbitrary choice of message size, content, and purpose
Simple hardware and interfacing
Hardware implementation for subs only requires a selectable shift register
Subs use the main's clock and hence do not need precision oscillators
Subs do not need a unique address unlike I²C or GPIB or SCSI
Mains only additionally require generation of clock and signals
Results in simple bit-banged software implementation
Uses only four pins on IC packages, and wires in board layouts or connectors, much fewer than parallel interfaces
At most one unique signal per device (); all others are shared
Note: the daisy-chain configuration doesn't need more than one shared
Typically lower power requirements than I²C or SMBus due to less circuitry (including pull up resistors)
Single main means no bus arbitration (and associated failure modes) - unlike CAN-bus
Transceivers are not needed - unlike CAN-bus
Signals are unidirectional, allowing for easy galvanic isolation
Disadvantages
Requires more pins on IC packages than I²C, even in three-wire variants
Only handles short distances compared to RS-232, RS-485, or CAN-bus (though distance can be extended with the use of transceivers like RS-422)
Extensibility severely reduced when multiple subs using different SPI Modes are required
Access is slowed down when main frequently needs to reinitialize in different modes
No formal standard
So validating conformance is not possible
Many existing variations complicate support
No built-in protocol support for some conveniences:
No hardware flow control by the sub (but the main can delay the next clock edge to slow the transfer rate)
No hardware sub acknowledgment (the main could be transmitting to nowhere and not know it)
No error-checking protocol
No hot swapping (dynamically adding nodes)
Interrupts are outside the scope of SPI (see )
Applications
SPI is used to talk to a variety of peripherals, such as
Sensors: temperature, pressure, ADC, touchscreens, video game controllers
Control devices: audio codecs, digital potentiometers, DACs
Camera lenses: Canon EF lens mount
Communications: Ethernet, USB, USART, CAN, IEEE 802.15.4, IEEE 802.11
Memory: flash and EEPROMs
Real-time clocks
LCDs, sometimes even for managing image data
Any MMC or SD card (including SDIO variant)
Shift registers for additional I/O
Board real estate and wiring savings compared to a parallel bus are significant, and have earned SPI a solid role in embedded systems. That is true for most system-on-a-chip processors, both with higher-end 32-bit processors such as those using ARM, MIPS, or PowerPC and with lower-end microcontrollers such as the AVR, PIC, and MSP430. These chips usually include SPI controllers capable of running in either main or sub mode. In-system programmable AVR controllers (including blank ones) can be programmed using SPI.
Chip or FPGA based designs sometimes use SPI to communicate between internal components; on-chip real estate can be as costly as its on-board cousin. And for high-performance systems, FPGAs sometimes use SPI to interface as a sub to a host, as a main to sensors, or for flash memory used to bootstrap if they are SRAM-based.
The full-duplex capability makes SPI very simple and efficient for single main/single sub applications. Some devices use the full-duplex mode to implement an efficient, swift data stream for applications such as digital audio, digital signal processing, or telecommunications channels, but most off-the-shelf chips stick to half-duplex request/response protocols.
Variations
SPI implementations have a wide variety of protocol variations. Some devices are transmit-only; others are receive-only. Chip selects are sometimes active-high rather than active-low. Some devices send the least-significant bit first. Signal levels depend entirely on the chips involved. And while the baseline SPI protocol has no command codes, every device may define its own protocol of command codes. Some variations are minor or informal, while others have an official defining document and may be considered to be separate but related protocols.
Original definition
Motorola in 1983 listed three 6805 8-bit microcomputers that have an integrated "Serial Peripheral Interface", whose functionality is described in a 1984 manual.
AN991
Motorola's 1987 Application Node AN991 "Using the Serial Peripheral Interface to Communicate Between Multiple Microcomputers" (now under NXP, last revised 2002) informally serves as the "official" defining document for SPI.
Timing variations
Some devices have timing variations from Motorola's CPOL/CPHA modes. Sending data from sub to main may use the opposite clock edge as main to sub. Devices often require extra clock idle time before the first clock or after the last one, or between a command and its response.
Some devices have two clocks, one to read data, and another to transmit it into the device. Many of the read clocks run from the chip select line.
Transmission size
Different transmission word sizes are common. Many SPI chips only support messages that are multiples of 8 bits. Such chips can not interoperate with the JTAG or SGPIO protocols, or any other protocol that requires messages that are not multiples of 8 bits.
No chip select
Some devices don't use chip select, and instead manage protocol state machine entry/exit using other methods.
Connectors
Anyone needing an external connector for SPI defines their own or uses another standard connection such as: UEXT, Pmod, various JTAG connectors, Secure Digital card socket, etc.
Flow control
Some devices require an additional flow control signal from sub to main, indicating when data is ready. This leads to a 5-wire protocol instead of the usual 4. Such a ready or enable signal is often active-low, and needs to be enabled at key points such as after commands or between words. Without such a signal, data transfer rates may need to be slowed down significantly, or protocols may need to have dummy bytes inserted, to accommodate the worst case for the sub response time. Examples include initiating an ADC conversion, addressing the right page of flash memory, and processing enough of a command that device firmware can load the first word of the response. (Many SPI mains do not support that signal directly, and instead rely on fixed delays.)
SafeSPI
SafeSPI is an industry standard for SPI in automotive applications. Its main focus is the transmission of sensor data between different devices.
High reliability modifications
In electrically noisy environments, since SPI has few signals, it can be economical to reduce the effects of common mode noise by adapting SPI to use low-voltage differential signaling. Another advantage is that the controlled devices can be designed to loop-back to test signal integrity.
Intelligent SPI controllers
A Queued Serial Peripheral Interface (QSPI; different to but has same abbreviation as Quad SPI described in ) is a type of SPI controller that uses a data queue to transfer data across an SPI bus. It has a wrap-around mode allowing continuous transfers to and from the queue with only intermittent attention from the CPU. Consequently, the peripherals appear to the CPU as memory-mapped parallel devices. This feature is useful in applications such as control of an A/D converter. Other programmable features in Queued SPI are chip selects and transfer length/delay.
SPI controllers from different vendors support different feature sets; such direct memory access (DMA) queues are not uncommon, although they may be associated with separate DMA engines rather than the SPI controller itself, such as used by Multichannel Buffered Serial Port (MCBSP). Most SPI main controllers integrate support for up to four chip selects, although some require chip selects to be managed separately through GPIO lines.
Note that Queued SPI is different from Quad SPI, and some processors even confusingly allow a single "QSPI" interface to operate in either quad or queued mode!
Microwire
Microwire, often spelled μWire, is essentially a predecessor of SPI and a trademark of National Semiconductor. It's a strict subset of SPI: half-duplex, and using SPI mode 0. Microwire chips tend to need slower clock rates than newer SPI versions; perhaps 2 MHz vs. 20 MHz. Some Microwire chips also support a three-wire mode.
Microwire/Plus
Microwire/Plus is an enhancement of Microwire and features full-duplex communication and support for SPI modes 0 and 1. There was no specified improvement in serial clock speed.
Three-wire
Three-wire variants of SPI restricted to a half-duplex mode use a single bidirectional data line called SISO (sub out/sub in) or MOMI (main out/main in) instead of SPI's two unidirectional lines (MOSI and MISO). Three-wire tends to be used for lower-performance parts, such as small EEPROMs used only during system startup, certain sensors, and Microwire. Few SPI controllers support this mode, although it can be easily bit-banged in software.
Dual SPI
For instances where the full-duplex nature of SPI is not used, an extension uses both data pins in a half-duplex configuration to send two bits per clock cycle. Typically a command byte is sent requesting a response in dual mode, after which the MOSI line becomes SIO0 (serial I/O 0) and carries even bits, while the MISO line becomes SIO1 and carries odd bits. Data is still transmitted most-significant bit first, but SIO1 carries bits 7, 5, 3 and 1 of each byte, while SIO0 carries bits 6, 4, 2 and 0.
This is particularly popular among SPI ROMs, which have to send a large amount of data, and comes in two variants:
Dual read sends the command and address from the main in single mode, and returns the data in dual mode.
Dual I/O sends the command in single mode, then sends the address and return data in dual mode.
Quad SPI
Quad SPI (QSPI; different to but has same abbreviation as Queued-SPI described in ) goes beyond dual SPI, adding two more I/O lines (SIO2 and SIO3) and sends 4 data bits per clock cycle. Again, it is requested by special commands, which enable quad mode after the command itself is sent in single mode.
SQI Type 1 Commands sent on single line but addresses and data sent on four lines
SQI Type 2 Commands and addresses sent on a single line but data sent/received on four lines
QPI/SQI
Further extending quad SPI, some devices support a "quad everything" mode where all communication takes place over 4 data lines, including commands. This is variously called "QPI" (not to be confused with Intel QuickPath Interconnect) or "serial quad I/O" (SQI)
This requires programming a configuration bit in the device and requires care after reset to establish communication.
Double data rate
In addition to using multiple lines for I/O, some devices increase the transfer rate by using double data rate transmission.
JTAG
Although there are some similarities between SPI and the JTAG (IEEE 1149.1-2013) protocol, they are not interchangeable. JTAG is specifically intended to provide reliable test access to the I/O pins from an off-board controller with less precise signal delay and skew parameters, while SPI has many varied applications. While not strictly a level sensitive interface, the JTAG protocol supports the recovery of both setup and hold violations between JTAG devices by reducing the clock rate or changing the clock's duty cycles. Consequently, the JTAG interface is not intended to support extremely high data rates.
SGPIO
SGPIO is essentially another (incompatible) application stack for SPI designed for particular backplane management activities. SGPIO uses 3-bit messages.
Intel's Enhanced Serial Peripheral Interface
Intel has developed a successor to its Low Pin Count (LPC) bus that it calls the Enhanced Serial Peripheral Interface (eSPI) bus. Intel aims to reduce the number of pins required on motherboards and increase throughput compared to LPC, reduce the working voltage to 1.8 volts to facilitate smaller chip manufacturing processes, allow eSPI peripherals to share SPI flash devices with the host (the LPC bus did not allow firmware hubs to be used by LPC peripherals), tunnel previous out-of-band pins through eSPI, and allow system designers to trade off cost and performance.
An eSPI bus can either be shared with SPI devices to save pins or be separate from an SPI bus to allow more performance, especially when eSPI devices need to use SPI flash devices.
This standard defines an Alert# signal that is used by an eSPI sub to request service from the main. In a performance-oriented design or a design with only one eSPI sub, each eSPI sub will have its Alert# pin connected to an Alert# pin on the eSPI main that is dedicated to each sub, allowing the eSPI main to grant low-latency service, because the eSPI main will know which eSPI sub needs service and will not need to poll all of the subs to determine which device needs service. In a budget design with more than one eSPI sub, all of the Alert# pins of the subs are connected to one Alert# pin on the eSPI main in a wired-OR connection, which requires the main to poll all the subs to determine which ones need service when the Alert# signal is pulled low by one or more peripherals that need service. Only after all of the devices are serviced will the Alert# signal be pulled high due to none of the eSPI subs needing service and therefore pulling the Alert# signal low.
This standard allows designers to use 1-bit, 2-bit, or 4-bit communications at speeds from 20 to 66 MHz to further allow designers to trade off performance and cost.
Communications that were out-of-band of LPC like general-purpose input/output (GPIO) and System Management Bus (SMBus) should be tunneled through eSPI via virtual wire cycles and out-of-band message cycles respectively in order to remove those pins from motherboard designs using eSPI.
This standard supports standard memory cycles with lengths of 1 byte to 4 kilobytes of data, short memory cycles with lengths of 1, 2, or 4 bytes that have much less overhead compared to standard memory cycles, and I/O cycles with lengths of 1, 2, or 4 bytes of data which are low overhead as well. This significantly reduces overhead compared to the LPC bus, where all cycles except for the 128-byte firmware hub read cycle spends more than one-half of all of the bus's throughput and time in overhead. The standard memory cycle allows a length of anywhere from 1 byte to 4 kilobytes in order to allow its larger overhead to be amortised over a large transaction. eSPI subs are allowed to initiate bus master versions of all of the memory cycles. Bus master I/O cycles, which were introduced by the LPC bus specification, and ISA-style DMA including the 32-bit variant introduced by the LPC bus specification, are not present in eSPI. Therefore, bus master memory cycles are the only allowed DMA in this standard.
eSPI subs are allowed to use the eSPI main as a proxy to perform flash operations on a standard SPI flash memory sub on behalf of the requesting eSPI sub.
64-bit memory addressing is also added, but is only permitted when there is no equivalent 32-bit address.
The Intel Z170 chipset can be configured to implement either this bus or a variant of the LPC bus that is missing its ISA-style DMA capability and is underclocked to 24 MHz instead of the standard 33 MHz.
The eSPI bus is also adopted by AMD Ryzen chipsets.
Development tools
Single-board computers
Single-board computers may provide pin access to SPI hardware units. For instance, the Raspberry Pi's J8 header exposes at least two SPI units that can be used via Linux drivers or python.
USB to SPI adapters
There are a number of USB adapters that allow a desktop PC or smartphone with USB to communicate with SPI chips (e.g. FT221xs). They are used for embedded systems, chips (FPGA, ASIC, and SoC) and peripheral testing, programming and debugging. Many of them also provide scripting or programming capabilities (e.g. Visual Basic, C/C++, VHDL).
The key SPI parameters are: the maximum supported frequency for the serial interface, command-to-command latency, and the maximum length for SPI commands. It is possible to find SPI adapters on the market today that support up to 100 MHz serial interfaces, with virtually unlimited access length.
SPI protocol being a de facto standard, some SPI host adapters also have the ability of supporting other protocols beyond the traditional 4-wire SPI (for example, support of quad-SPI protocol or other custom serial protocol that derive from SPI).
Protocol analyzers
Logic analyzers are tools which collect, timestamp, analyze, decode, store, and view the high-speed waveforms, to help debug and develop. Most logic analyzers have the capability to decode SPI bus signals into high-level protocol data with human-readable labels.
Oscilloscopes
SPI waveforms can be seen on analog channels (and/or via digital channels in mixed-signal oscilloscopes). Most oscilloscope vendors offer optional support for SPI protocol analysis (both 2-, 3-, and 4-wire SPI) with triggering.
Alternative terminology
Various alternative abbreviations for the four common SPI signals are used. (This section omits overbars indicating active-low.)
Serial clock
SCK, SCLK, CLK, SCL
Main out, sub in (MOSI)
SIMO, MTSR, SPID - correspond to MOSI on both main and sub devices, connects to each other
SDI, DI, DIN, SI, SDA - on sub devices; various abbreviations for serial data in; connects to MOSI on main
SDO, DO, DOUT, SO - on main devices; various abbreviations for serial data out; connects to MOSI on sub
COPI, PICO for peripheral and controller, or COTI for controller and target
Main in, sub out (MISO)
SOMI, MRST, SPIQ - correspond to MISO on both main and sub devices, connects to each other
SDO, DO, DOUT, SO - on sub devices; connects to MISO on main
SDI, DI, DIN, SI - on main devices; connects to MISO on sub
CIPO, POCI, or CITO
Chip select (CS)
CE (chip enable)
Historical: SS (slave select), SSEL, NSS, /SS, SS# (sub select)
Microchip uses host and client though keeps the abbreviation MOSI and MISO.
See also
List of network buses
Notes
References
External links
Intel eSPI (Enhanced Serial Peripheral Interface)
SPI Tutorial
Interfaces
Computer buses
Computer hardware standards
Serial buses | Serial Peripheral Interface | [
"Technology"
] | 6,742 | [
"Computer standards",
"Computer hardware standards",
"Interfaces"
] |
340,606 | https://en.wikipedia.org/wiki/Nilometer | A nilometer is a structure for measuring the Nile River's clarity and water level during the annual flood season in Egypt. There were three main types of nilometers, calibrated in Egyptian cubits: (1) a vertical column, (2) a corridor stairway of steps leading down to the Nile, and (3) a deep well with a culvert. If the water level was low, the fertility of the floodplain would suffer. If it was too high, the flooding would be destructive. There was a specific mark that indicated how high the flood should be if the fields were to get good soil.
Nilometers originated in pharaonic times, were also built in Roman times, and were highly prevalent in Islamic Egypt in Rashidun, Ummayad, Abbasid, Tulunid, Mamluk, Alawiyya and Republican periods, until the Aswan Dam rendered them obsolete in the 1960s.
Description
Between July and November, the reaches of the Nile running through Egypt would burst their banks and cover the adjacent floodplain. When the waters receded, around September or October, they left behind a rich alluvial deposit of exceptionally fertile black silt over the croplands. The akhet, or Season of the Inundation, was one of the three seasons into which the ancient Egyptians divided their year.
The annual flood was of great importance to Egyptian civilization. A moderate inundation was a vital part of the agricultural cycle; however, a lighter inundation than normal would cause famine, and too much flood water would be equally disastrous, washing away much of the infrastructure built on the flood plain. Records from AD 622999 indicate that, on average, 28% of the years saw an inundation that fell short of expectations.
Across Egypt various nilometers could be found that recorded readings of the Nile's annual levels. A fragment of a recovered Egyptian stele "Royal Annals of the Old Kingdom" known as the "Palermo stone" deemed to be from the times of the First Dynasty around 3,000 B.C.E. The Palermo Stone reports systems of measurements utilizing units such as cubits, palms, and fingers.
The ability to predict the volume of the coming inundation was part of the mystique of the ancient Egyptian priesthood. The same skill also played a political and administrative role, since the quality of the year's flood was used to determine the levels of tax to be paid. This is where the nilometer came into play, with priests monitoring the day-to-day level of the river and announcing the awaited arrival of the summer flood.
Religious attributes related to the Nile intertwined with the ideology or belief in Ma'at (a system of natural balance). Nilometers were accessible to only members of the city's priests and nobles. The restriction on who may access these structures ensured both accountability in proper readings and political control for the religious communities and ruling classes.
Designs
The simplest nilometer design is a vertical column submerged in the waters of the river, with marked intervals indicating the depth of the water. One that follows this simple design, albeit housed in an elaborate and ornate stone structure, can still be seen on the island of Roda in central Cairo This nilometer visible today dates as far back as AD 861, when the Abbasid caliph al-Mutawakkil ordered its construction, overseen by the astronomer al-Farghani. Another nilometer had been ordered in 715 by Usāma b. Zayd b. ʿAdī, who was in charge of collecting the land tax (kharaj) in Egypt for the Umayyad caliph Sulaymān ibn ʿAbd al-Malik.
The second nilometer design comprises a flight of stairs leading down into the water, with depth markings along the walls. The best known example of this kind can be seen on Elephantine in Aswan, where a stairway of 52 steps leads down to a doorway at the Nile. This location was also particularly important, since for much of Egyptian history, Elephantine marked Egypt's southern border and was therefore the first place where the onset of the annual flood was detected.
The most elaborate design involved a canal or culvert that led from the riverbank – often running for a considerable distance – and then fed a well, tank, or cistern. These nilometer wells were most frequently located within the confines of temples, where only the priests and rulers were allowed access. A particularly fine example, with a deep, cylindrical well and a culvert opening in the surrounding wall, can be seen at the Temple of Kom Ombo, to the north of Aswan.
History
While nilometers originated in Pharaonic times, they continued to be used by the later civilizations that held sway in Egypt. Some were constructed in Roman times. In the 20th century, the Nile's annual inundation was first greatly reduced, and then eliminated entirely, with the construction of the Aswan dams. While the Aswan High Dam's impact on Egypt and its agriculture has been controversial for other, more complex reasons, it has also had the additional effect of rendering the nilometer obsolete.
Roda Island
The first nilometer on Roda Island was constructed by Usama bin Zayd bin Adl before Jumada II, 96 AH (February 715), during the reign of the Umayyad caliph al-Walid. The 14th-century Arabic historian Maqrīzī claims that the construction cost 24,000 dirhams. During the reign of Sulayman ibn Abd al-Malik, Usama wrote to the caliph informing him of the dilapidated state of the nilometer. He received a reply ordering him to construct a new one, which he did in 97 AH (5 September 715—24 August 716). Yaqut al-Hamawi, writing in the 12th–13th centuries, claims that in the beginning of year 247 AH (March 861), during Yazid ibn Abd Allah al-Turki's governorship of Egypt, the Abbasid caliph al-Mutawakkil had the 'new' nilometer constructed and ordered that the privilege of measuring the river 'be taken away from the Christians.' The governor then appointed a man from Basra named Abu'r-Raddad who had emigrated to Egypt and taught hadith. He died in 266 AH (879/80), with Yaqut claiming 'the supervision of the Nilometer has remained in the hands of his descendants until the present day' (which would have been around 1225 for the author). Ibn Khallikan, a 13th-century historian, gives a different account of this nilometer, recounting that a 'pious' muezzin in the old Mosque of Amr wished to carve inscriptions in various places of the nilometer. After consulting with Yazid ibn Abd Allah, Sulayman ibn Wahb and Hasan al-Khadim, the muezzin proposed to inscribe various Qu'ranic passages in the name of al-Mutawakkil. Sulayman ibn Wahb then wrote to the caliph, who replied in writing to choose verses of the Qu'ran 'most appropriate' to the nilometer and to inscribe the caliph's name.
Ibn Khallikan writes that the architect of the nilometer was Ahmad ibn Muhammad al-Hasib. Abu Ja'far al-Katib and Ibn Abi Usaybi'a mention that Ahmad ibn Kathir al-Farghani was sent to Fustat by al-Mutawakkil to supervise the construction. Abu al-Mahasin Yusuf (d. 1604) makes the same statement but calls him Muhammad ibn Kathir al-Farghani (full name: Abu'l-Abbas Ahmad ibn Muhammad ibn Kathir al-Farghani). For this reason, Gaston Wiet and Creswell argue that the al-Farghani and al-Hasib are the same person.
In 872–3 (259 AH), Ahmad ibn Tulun, the autonomous ruler of Egypt, would also have the nilometer restored. Al-Mutawakkil's name was removed from the Kufic inscription of the nilometer. K. A. C. Creswell states that the main inscription of the nilometer was probably tampered with by Ibn Tulun, saying "there can be little doubt that it was he who removed the name of the Abbasid Khalif." Ibn Tulun would however refrain from substituting his own name, with Creswell claiming as he did not feel sufficiently secure to do so. The first Tulunid Emir during 872-873 would spend 1,000 dinars on works carried out on the nilometer. Consequently, according to Abdul Rofik Bruno, the Nile's irrigation would be enhanced, and agricultural output increased.
Amr ibn al-As after the conquest of Egypt reported to the Caliph Umar that when the Nile rose to 14 cubits there was a sufficient harvest, 16 an abundant harvest, 17 being the most advantageous height of all, and that at 18, one-fourth of Egypt would be inundated and usually be followed by plague. The Baghdad doctor, Abd al-Latif al-Baghdadi who traveled Egypt between 1192-1201 would also relate similar measurements. In the exceedingly low water levels of 1201 and 1202, the nilometer remained dry. In 1201, the year commenced with a rise in 2 cubits before rising an average 15¹⁶⁄₂₄ cubits. In 1202, the year began with 1½ cubits before rising to 15²³⁄₂₄ cubits. During the Abbasid Period, the nilometer was used to measure the river level and hence determine the rates of tax in Egypt.
In 1937, efforts to drain and excavate the nilometer were begun by Kamil Bey Ghalib, the Under-Secretary of State for Public Works, employing a new method used by Rothpletz and Lienhard. In this method, the mud could be removed completely and the structure examined.
See also
Hunger stone
Notes
References
Architecture in Egypt
Measuring instruments
Nile
Water supply
Hydrology instrumentation | Nilometer | [
"Chemistry",
"Technology",
"Engineering",
"Environmental_science"
] | 2,130 | [
"Hydrology",
"Hydrology instrumentation",
"Measuring instruments",
"Environmental engineering",
"Water supply"
] |
340,617 | https://en.wikipedia.org/wiki/List%20of%20complex%20analysis%20topics | Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.
See also: glossary of real and complex analysis.
Overview
Complex numbers
Complex plane
Complex functions
Complex derivative
Holomorphic functions
Harmonic functions
Elementary functions
Polynomial functions
Exponential functions
Trigonometric functions
Hyperbolic functions
Logarithmic functions
Inverse trigonometric functions
Inverse hyperbolic functions
Residue theory
Isometries in the complex plane
Related fields
Number theory
Hydrodynamics
Thermodynamics
Electrical engineering
Local theory
Holomorphic function
Antiholomorphic function
Cauchy–Riemann equations
Conformal mapping
Conformal welding
Power series
Radius of convergence
Laurent series
Meromorphic function
Entire function
Pole (complex analysis)
Zero (complex analysis)
Residue (complex analysis)
Isolated singularity
Removable singularity
Essential singularity
Branch point
Principal branch
Weierstrass–Casorati theorem
Landau's constants
Holomorphic functions are analytic
Schwarzian derivative
Analytic capacity
Disk algebra
Univalent function
Growth and distribution of values
Ahlfors theory
Bieberbach conjecture
Borel–Carathéodory theorem
Corona theorem
Hadamard three-circle theorem
Hardy space
Hardy's theorem
Maximum modulus principle
Nevanlinna theory
Paley–Wiener theorem
Progressive function
Value distribution theory of holomorphic functions
Contour integrals
Line integral
Cauchy's integral theorem
Cauchy's integral formula
Residue theorem
Liouville's theorem (complex analysis)
Examples of contour integration
Fundamental theorem of algebra
Simply connected
Winding number
Principle of the argument
Rouché's theorem
Bromwich integral
Morera's theorem
Mellin transform
Kramers–Kronig relation, a. k. a. Hilbert transform
Sokhotski–Plemelj theorem
Special functions
Exponential function
Beta function
Gamma function
Riemann zeta function
Riemann hypothesis
Generalized Riemann hypothesis
Elliptic function
Half-period ratio
Jacobi's elliptic functions
Weierstrass's elliptic functions
Theta function
Elliptic modular function
J-function
Modular function
Modular form
Riemann surfaces
Analytic continuation
Riemann sphere
Riemann surface
Riemann mapping theorem
Carathéodory's theorem (conformal mapping)
Riemann–Roch theorem
Other
Amplitwist
Antiderivative (complex analysis)
Bôcher's theorem
Cayley transform
Harmonic conjugate
Hilbert's inequality
Method of steepest descent
Montel's theorem
Periodic points of complex quadratic mappings
Pick matrix
Runge approximation theorem
Schwarz lemma
Weierstrass factorization theorem
Mittag-Leffler's theorem
Sendov's conjecture
Infinite compositions of analytic functions
Several complex variables
Biholomorphy
Cartan's theorems A and B
Cousin problems
Edge-of-the-wedge theorem
Several complex variables
History
People
Augustin Louis Cauchy
Leonhard Euler
Carl Friedrich Gauss
Jacques Hadamard
Kiyoshi Oka
Bernhard Riemann
Karl Weierstrass
Pierre Alphonse Laurent
Brook Taylor
Siméon Denis Poisson
Hermann Schwarz
Camille Jordan
Carl Gustav Jacob Jacobi
Eugène Rouché
Gerardus Mercator
Joseph Liouville
Pierre-Simon Laplace
August Ferdinand Möbius
William Kingdon Clifford
Complex analysis
Complex analysis
Complex analysis | List of complex analysis topics | [
"Mathematics"
] | 673 | [
"nan"
] |
340,621 | https://en.wikipedia.org/wiki/George%20Boolos | George Stephen Boolos (; September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
Life
Boolos was of Greek-Jewish descent (Boolos is an Arabic form of the name Paulus/Paûlos common among Arabic speaking Greek Orthodox community). He graduated with an A.B. in mathematics from Princeton University after completing a senior thesis, titled "A simple proof of Gödel's first incompleteness theorem", under the supervision of Raymond Smullyan. Oxford University awarded him the B.Phil. in 1963. In 1966, he obtained the first PhD in philosophy ever awarded by the Massachusetts Institute of Technology, under the direction of Hilary Putnam. After teaching three years at Columbia University, he returned to MIT in 1969, where he spent the rest of his career.
A charismatic speaker well known for his clarity and wit, he once delivered a lecture (1994b) giving an account of Gödel's second incompleteness theorem, employing only words of one syllable. At the end of his viva, Hilary Putnam asked him, "And tell us, Mr. Boolos, what does the analytical hierarchy have to do with the real world?" Without hesitating Boolos replied, "It's part of it". An expert on puzzles of all kinds, in 1993 Boolos reached the London Regional Final of The Times crossword competition. His score was one of the highest ever recorded by an American. He wrote a paper on "The Hardest Logic Puzzle Ever"—one of many puzzles created by Raymond Smullyan.
Boolos died of pancreatic cancer on 27 May 1996.
Work
Boolos coauthored with Richard Jeffrey the first three editions of the classic university text on mathematical logic, Computability and Logic. The book is now in its fifth edition, the last two editions updated by John P. Burgess.
Kurt Gödel wrote the first paper on provability logic, which applies modal logic—the logic of necessity and possibility—to the theory of mathematical proof, but Gödel never developed the subject to any significant extent. Boolos was one of its earliest proponents and pioneers, and he produced the first book-length treatment of it, The Unprovability of Consistency, published in 1979. The solution of a major unsolved problem some years later led to a new treatment, The Logic of Provability, published in 1993. The modal-logical treatment of provability helped demonstrate the "intensionality" of Gödel's Second Incompleteness Theorem, meaning that the theorem's correctness depends on the precise formulation of the provability predicate. These conditions were first identified by David Hilbert and Paul Bernays in their Grundlagen der Arithmetik. The unclear status of the Second Theorem was noted for several decades by logicians such as Georg Kreisel and Leon Henkin, who asked whether the formal sentence expressing "This sentence is provable" (as opposed to the Gödel sentence, "This sentence is not provable") was provable and hence true. Martin Löb showed Henkin's conjecture to be true, as well as identifying an important "reflection" principle also neatly codified using the modal logical approach. Some of the key provability results involving the representation of provability predicates had been obtained earlier using very different methods by Solomon Feferman.
Boolos was an authority on the 19th-century German mathematician and philosopher Gottlob Frege. Boolos proved a conjecture due to Crispin Wright (and also proved, independently, by others), that the system of Frege's Grundgesetze, long thought vitiated by Russell's paradox, could be freed of inconsistency by replacing one of its axioms, the notorious Basic Law V with Hume's Principle. The resulting system has since been the subject of intense work.
Boolos argued that if one reads the second-order variables in monadic second-order logic plurally, then second-order logic can be interpreted as having no ontological commitment to entities other than those over which the first-order variables range. The result is plural quantification. David Lewis employed plural quantification in his Parts of Classes to derive a system in which Zermelo–Fraenkel set theory and the Peano axioms were all theorems. While Boolos is usually credited with plural quantification, Peter Simons (1982) has argued that the essential idea can be found in the work of Stanislaw Leśniewski.
Shortly before his death, Boolos chose 30 of his papers to be published in a book. The result is perhaps his most highly regarded work, his posthumous Logic, Logic, and Logic. This book reprints much of Boolos's work on the rehabilitation of Frege, as well as a number of his papers on set theory, second-order logic and nonfirstorderizability, plural quantification, proof theory, and three short insightful papers on Gödel's Incompleteness Theorem. There are also papers on Dedekind, Cantor, and Russell.
Publications
Books
1979. The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.
1990 (editor). Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge University Press.
1993. The Logic of Provability. Cambridge University Press.
1998 (Richard Jeffrey and John P. Burgess, eds.). Logic, Logic, and Logic Harvard University Press.
2007 (1974) (with Richard Jeffrey and John P. Burgess). Computability and Logic, 4th ed. Cambridge University Press.
Articles
LLL = reprinted in Logic, Logic, and Logic.
FPM = reprinted in Demopoulos, W., ed., 1995. Frege's Philosophy of Mathematics. Harvard Univ. Press.
1968 (with Hilary Putnam), "Degrees of unsolvability of constructible sets of integers," Journal of Symbolic Logic 33: 497–513.
1969, "Effectiveness and natural languages" in Sidney Hook, ed., Language and Philosophy. New York University Press.
1970, "On the semantics of the constructible levels," 16: 139–148.
1970a, "A proof of the Löwenheim–Skolem theorem," Notre Dame Journal of Formal Logic 11: 76–78.
1971, "The iterative conception of set," Journal of Philosophy 68: 215–231. Reprinted in Paul Benacerraf and Hilary Putnam, eds.,1984. Philosophy of Mathematics: Selected Readings, 2nd ed. Cambridge Univ. Press: 486–502. LLL
1973, "A note on Evert Willem Beth's theorem," Bulletin de l'Academie Polonaise des Sciences 2: 1–2.
1974, "Arithmetical functions and minimization," Zeitschrift für mathematische Logik und Grundlagen der Mathematik 20: 353–354.
1974a, "Reply to Charles Parsons' 'Sets and classes'." First published in LLL.
1975, "Friedman's 35th problem has an affirmative solution," Notices of the American Mathematical Society 22: A-646.
1975a, "On Kalmar's consistency proof and a generalization of the notion of omega-consistency," Archiv für Mathematische Logik und Grundlagenforschung 17: 3–7.
1975b, "On second-order logic," Journal of Philosophy 72: 509–527. LLL.
1976, "On deciding the truth of certain statements involving the notion of consistency," Journal of Symbolic Logic 41: 779–781.
1977, "On deciding the provability of certain fixed point statements," Journal of Symbolic Logic 42: 191–193.
1979, "Reflection principles and iterated consistency assertions," Journal of Symbolic Logic 44: 33–35.
1980, "Omega-consistency and the diamond," Studia Logica 39: 237–243.
1980a, "On systems of modal logic with provability interpretations," Theoria 46: 7–18.
1980b, "Provability in arithmetic and a schema of Grzegorczyk," Fundamenta Mathematicae 106: 41–45.
1980c, "Provability, truth, and modal logic," Journal of Philosophical Logic 9: 1–7.
1980d, Review of Raymond M. Smullyan, What is the Name of This Book? The Philosophical Review 89: 467–470.
1981, "For every A there is a B," Linguistic Inquiry 12: 465–466.
1981a, Review of Robert M. Solovay, Provability Interpretations of Modal Logic," Journal of Symbolic Logic 46: 661–662.
1982, "Extremely undecidable sentences," Journal of Symbolic Logic 47: 191–196.
1982a, "On the nonexistence of certain normal forms in the logic of provability," Journal of Symbolic Logic 47: 638–640.
1984, "Don't eliminate cut," Journal of Philosophical Logic 13: 373–378. LLL.
1984a, "The logic of provability," American Mathematical Monthly 91: 470–480.
1984b, "Nonfirstorderizability again," Linguistic Inquiry 15: 343.
1984c, "On 'Syllogistic inference'," Cognition 17: 181–182.
1984d, "To be is to be the value of a variable (or some values of some variables)," Journal of Philosophy 81: 430–450. LLL.
1984e, "Trees and finite satisfiability: Proof of a conjecture of John Burgess," Notre Dame Journal of Formal Logic 25: 193–197.
1984f, "The justification of mathematical induction," PSA 2: 469–475. LLL.
1985, "1-consistency and the diamond," Notre Dame Journal of Formal Logic 26: 341–347.
1985a, "Nominalist Platonism," The Philosophical Review 94: 327–344. LLL.
1985b, "Reading the Begriffsschrift," Mind 94: 331–344. LLL; FPM: 163–81.
1985c (with Giovanni Sambin), "An incomplete system of modal logic," Journal of Philosophical Logic 14: 351–358.
1986, Review of Yuri Manin, A Course in Mathematical Logic, Journal of Symbolic Logic 51: 829–830.
1986–87, "Saving Frege from contradiction," Proceedings of the Aristotelian Society 87: 137–151. LLL; FPM 438–52.
1987, "The consistency of Frege's Foundations of Arithmetic" in J. J. Thomson, ed., 1987. On Being and Saying: Essays for Richard Cartwright. MIT Press: 3–20. LLL; FPM: 211–233.
1987a, "A curious inference," Journal of Philosophical Logic 16: 1–12. LLL.
1987b, "On notions of provability in provability logic," Abstracts of the 8th International Congress of Logic, Methodology and Philosophy of Science 5: 236–238.
1987c (with Vann McGee), "The degree of the set of sentences of predicate provability logic that are true under every interpretation," Journal of Symbolic Logic 52: 165–171.
1988, "Alphabetical order," Notre Dame Journal of Formal Logic 29: 214–215.
1988a, Review of Craig Smorynski, Self-Reference and Modal Logic, Journal of Symbolic Logic 53: 306–309.
1989, "Iteration again," Philosophical Topics 17: 5–21. LLL.
1989a, "A new proof of the Gödel incompleteness theorem," Notices of the American Mathematical Society 36: 388–390. LLL. An afterword appeared under the title "A letter from George Boolos," ibid., p. 676. LLL.
1990, "On 'seeing' the truth of the Gödel sentence," Behavioral and Brain Sciences 13: 655–656. LLL.
1990a, Review of Jon Barwise and John Etchemendy, Turing's World and Tarski's World, Journal of Symbolic Logic 55: 370–371.
1990b, Review of V. A. Uspensky, Gödel's Incompleteness Theorem, Journal of Symbolic Logic 55: 889–891.
1990c, "The standard of equality of numbers" in Boolos, G., ed., Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge Univ. Press: 261–278. LLL; FPM: 234–254.
1991, "Zooming down the slippery slope," Nous 25: 695–706. LLL.
1991a (with Giovanni Sambin), "Provability: The emergence of a mathematical modality," Studia Logica 50: 1–23.
1993, "The analytical completeness of Dzhaparidze's polymodal logics," Annals of Pure and Applied Logic 61: 95–111.
1993a, "Whence the contradiction?" Aristotelian Society Supplementary Volume 67: 213–233. LLL.
1994, "1879?" in P. Clark and B. Hale, eds. Reading Putnam. Oxford: Blackwell: 31–48. LLL.
1994a, "The advantages of honest toil over theft," in A. George, ed., Mathematics and Mind. Oxford University Press: 27–44. LLL.
1994b, "Gödel's second incompleteness theorem explained in words of one syllable," Mind 103: 1–3. LLL.
1995, "Frege's theorem and the Peano postulates," Bulletin of Symbolic Logic 1: 317–326. LLL.
1995a, "Introductory note to *1951" in Solomon Feferman et al., eds., Kurt Gödel, Collected Works, vol. 3. Oxford University Press: 290–304. LLL. *1951 is Gödel's 1951 Gibbs lecture, "Some basic theorems on the foundations of mathematics and their implications."
1995b, "Quotational ambiguity" in Leonardi, P., and Santambrogio, M., eds. On Quine. Cambridge University Press: 283–296. LLL
1996, "The Hardest Logic Puzzle Ever," Harvard Review of Philosophy 6: 62–65. LLL. Italian translation by Massimo Piattelli-Palmarini, "L'indovinello piu difficile del mondo," La Repubblica (16 April 1992): 36–37.
1996a, "On the proof of Frege's theorem" in A. Morton and S. P. Stich, eds., Paul Benacerraf and his Critics. Cambridge MA: Blackwell. LLL.
1997, "Constructing Cantorian counterexamples," Journal of Philosophical Logic 26: 237–239. LLL.
1997a, "Is Hume's principle analytic?" In Richard G. Heck, Jr., ed., Language, Thought, and Logic: Essays in Honour of Michael Dummett. Oxford Univ. Press: 245–61. LLL.
1997b (with Richard Heck), "Die Grundlagen der Arithmetik, §§82–83" in Matthias Schirn, ed., Philosophy of Mathematics Today. Oxford Univ. Press. LLL.
1998, "Gottlob Frege and the Foundations of Arithmetic." First published in LLL. French translation in Mathieu Marion and Alain Voizard eds., 1998. Frege. Logique et philosophie. Montréal and Paris: L'Harmattan: 17–32.
2000, "Must we believe in set theory?" in Gila Sher and Richard Tieszen, eds., Between Logic and Intuition: Essays in Honour of Charles Parsons. Cambridge University Press. LLL.
See also
American philosophy
Axiomatic set theory S of Boolos (1989)
General set theory, Boolos's axiomatic set theory just adequate for Peano and Robinson arithmetic.
List of American philosophers
Notes
References
Peter Simons (1982) "On understanding Lesniewski," History and Philosophy of Logic.
Solomon Feferman (1960) "Arithmetization of metamathematics in a general setting," Fundamentae Mathematica vol. 49, pp. 35–92.
External links
George Boolos Memorial Web Site
George Boolos. The hardest logic puzzle ever. The Harvard Review of Philosophy, 6:62–65, 1996.
1940 births
1996 deaths
20th-century American educators
20th-century American essayists
20th-century American historians
20th-century American Jews
20th-century American male writers
20th-century American mathematicians
20th-century American philosophers
Alumni of the University of Oxford
American historians of mathematics
American historians of philosophy
American male essayists
American male non-fiction writers
Analytic philosophers
Columbia University faculty
Deaths from pancreatic cancer in Massachusetts
American game theorists
History of logic
History of mathematics
Jewish American non-fiction writers
Jewish American historians
Jewish philosophers
Mathematical logicians
MIT School of Humanities, Arts, and Social Sciences faculty
American philosophers of logic
American philosophers of mathematics
American philosophy writers
Princeton University alumni
Puzzle designers
American set theorists
American people of Greek-Jewish descent | George Boolos | [
"Mathematics"
] | 3,651 | [
"Mathematical logic",
"Mathematical logicians"
] |
340,630 | https://en.wikipedia.org/wiki/Function%20space | In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space.
In linear algebra
Let be a field and let be any set. The functions → can be given the structure of a vector space over where the operations are defined pointwise, that is, for any , : → , any in , and any in , define
When the domain has additional structure, one might consider instead the subset (or subspace) of all such functions which respect that structure. For example, if and also itself are vector spaces over , the set of linear maps → form a vector space over with pointwise operations (often denoted Hom(,)). One such space is the dual space of : the set of linear functionals → with addition and scalar multiplication defined pointwise.
The cardinal dimension of a function space with no extra structure can be found by the Erdős–Kaplansky theorem.
Examples
Function spaces appear in various areas of mathematics:
In set theory, the set of functions from X to Y may be denoted {X → Y} or YX.
As a special case, the power set of a set X may be identified with the set of all functions from X to {0, 1}, denoted 2X.
The set of bijections from X to Y is denoted . The factorial notation X! may be used for permutations of a single set X.
In functional analysis, the same is seen for continuous linear transformations, including topologies on the vector spaces in the above, and many of the major examples are function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces.
In functional analysis, the set of all functions from the natural numbers to some set X is called a sequence space. It consists of the set of all possible sequences of elements of X.
In topology, one may attempt to put a topology on the space of continuous functions from a topological space X to another one Y, with utility depending on the nature of the spaces. A commonly used example is the compact-open topology, e.g. loop space. Also available is the product topology on the space of set theoretic functions (i.e. not necessarily continuous functions) YX. In this context, this topology is also referred to as the topology of pointwise convergence.
In algebraic topology, the study of homotopy theory is essentially that of discrete invariants of function spaces;
In the theory of stochastic processes, the basic technical problem is how to construct a probability measure on a function space of paths of the process (functions of time);
In category theory, the function space is called an exponential object or map object. It appears in one way as the representation canonical bifunctor; but as (single) functor, of type , it appears as an adjoint functor to a functor of type on objects;
In functional programming and lambda calculus, function types are used to express the idea of higher-order functions.
In domain theory, the basic idea is to find constructions from partial orders that can model lambda calculus, by creating a well-behaved Cartesian closed category.
In the representation theory of finite groups, given two finite-dimensional representations and of a group , one can form a representation of over the vector space of linear maps Hom(,) called the Hom representation.
Functional analysis
Functional analysis is organized around adequate techniques to bring function spaces as topological vector spaces within reach of the ideas that would apply to normed spaces of finite dimension. Here we use the real line as an example domain, but the spaces below exist on suitable open subsets
continuous functions endowed with the uniform norm topology
continuous functions with compact support
bounded functions
continuous functions which vanish at infinity
continuous functions that have r continuous derivatives.
smooth functions
smooth functions with compact support (i.e. the set of bump functions)
real analytic functions
, for , is the Lp space of measurable functions whose p-norm is finite
, the Schwartz space of rapidly decreasing smooth functions and its continuous dual, tempered distributions
compact support in limit topology
Sobolev space of functions whose weak derivatives up to order k are in
holomorphic functions
linear functions
piecewise linear functions
continuous functions, compact open topology
all functions, space of pointwise convergence
Hardy space
Hölder space
Càdlàg functions, also known as the Skorokhod space
, the space of all Lipschitz functions on that vanish at zero.
Norm
If is an element of the function space of all continuous functions that are defined on a closed interval , the norm defined on is the maximum absolute value of for ,
is called the uniform norm or supremum norm ('sup norm').
Bibliography
Kolmogorov, A. N., & Fomin, S. V. (1967). Elements of the theory of functions and functional analysis. Courier Dover Publications.
Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press.
See also
List of mathematical functions
Clifford algebra
Tensor field
Spectral theory
Functional determinant
References
Topology of function spaces
Linear algebra | Function space | [
"Mathematics"
] | 1,107 | [
"Function spaces",
"Vector spaces",
"Space (mathematics)",
"Linear algebra",
"Algebra"
] |
340,678 | https://en.wikipedia.org/wiki/Quantum%20group | In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups. Despite their name, they do not themselves have a natural group structure, though they are in some sense 'close' to a group.
The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a "bicrossproduct" class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.
In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.
Intuitive meaning
The discovery of quantum groups was quite unexpected since it was known for a long time that compact groups and semisimple Lie algebras are "rigid" objects, in other words, they cannot be "deformed". One of the ideas behind quantum groups is that if we consider a structure that is in a sense equivalent but larger, namely a group algebra or a universal enveloping algebra, then a group algebra or enveloping algebra can be "deformed", although the deformation will no longer remain a group algebra or enveloping algebra. More precisely, deformation can be accomplished within the category of Hopf algebras that are not required to be either commutative or cocommutative. One can think of the deformed object as an algebra of functions on a "noncommutative space", in the spirit of the noncommutative geometry of Alain Connes. This intuition, however, came after particular classes of quantum groups had already proved their usefulness in the study of the quantum Yang–Baxter equation and quantum inverse scattering method developed by the Leningrad School (Ludwig Faddeev, Leon Takhtajan, Evgeny Sklyanin, Nicolai Reshetikhin and Vladimir Korepin) and related work by the Japanese School. The intuition behind the second, bicrossproduct, class of quantum groups was different and came from the search for self-dual objects as an approach to quantum gravity.
Drinfeld–Jimbo type quantum groups
One type of objects commonly called a "quantum group" appeared in the work of Vladimir Drinfeld and Michio Jimbo as a deformation of the universal enveloping algebra of a semisimple Lie algebra or, more generally, a Kac–Moody algebra, in the category of Hopf algebras. The resulting algebra has additional structure, making it into a quasitriangular Hopf algebra.
Let A = (aij) be the Cartan matrix of the Kac–Moody algebra, and let q ≠ 0, 1 be a complex number, then the quantum group, Uq(G), where G is the Lie algebra whose Cartan matrix is A, is defined as the unital associative algebra with generators kλ (where λ is an element of the weight lattice, i.e. 2(λ, αi)/(αi, αi) is an integer for all i), and ei and fi (for simple roots, αi), subject to the following relations:
And for i ≠ j we have the q-Serre relations, which are deformations of the Serre relations:
where the q-factorial, the q-analog of the ordinary factorial, is defined recursively using q-number:
In the limit as q → 1, these relations approach the relations for the universal enveloping algebra U(G), where
and tλ is the element of the Cartan subalgebra satisfying (tλ, h) = λ(h) for all h in the Cartan subalgebra.
There are various coassociative coproducts under which these algebras are Hopf algebras, for example,
where the set of generators has been extended, if required, to include kλ for λ which is expressible as the sum of an element of the weight lattice and half an element of the root lattice.
In addition, any Hopf algebra leads to another with reversed coproduct T o Δ, where T is given by T(x ⊗ y) = y ⊗ x, giving three more possible versions.
The counit on Uq(A) is the same for all these coproducts: ε(kλ) = 1, ε(ei) = ε(fi) = 0, and the respective antipodes for the above coproducts are given by
Alternatively, the quantum group Uq(G) can be regarded as an algebra over the field C(q), the field of all rational functions of an indeterminate q over C.
Similarly, the quantum group Uq(G) can be regarded as an algebra over the field Q(q), the field of all rational functions of an indeterminate q over Q (see below in the section on quantum groups at q = 0). The center of quantum group can be described by quantum determinant.
Representation theory
Just as there are many different types of representations for Kac–Moody algebras and their universal enveloping algebras, so there are many different types of representation for quantum groups.
As is the case for all Hopf algebras, Uq(G) has an adjoint representation on itself as a module, with the action being given by
where
Case 1: q is not a root of unity
One important type of representation is a weight representation, and the corresponding module is called a weight module. A weight module is a module with a basis of weight vectors. A weight vector is a nonzero vector v such that kλ · v = dλv for all λ, where dλ are complex numbers for all weights λ such that
for all weights λ and μ.
A weight module is called integrable if the actions of ei and fi are locally nilpotent (i.e. for any vector v in the module, there exists a positive integer k, possibly dependent on v, such that for all i). In the case of integrable modules, the complex numbers dλ associated with a weight vector satisfy , where ν is an element of the weight lattice, and cλ are complex numbers such that
for all weights λ and μ,
for all i.
Of special interest are highest-weight representations, and the corresponding highest weight modules. A highest weight module is a module generated by a weight vector v, subject to kλ · v = dλv for all weights μ, and ei · v = 0 for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i.e. a module generated by a weight vector v, subject to kλ · v = dλv for all weights λ, and fi · v = 0 for all i.
Define a vector v to have weight ν if for all λ in the weight lattice.
If G is a Kac–Moody algebra, then in any irreducible highest weight representation of Uq(G), with highest weight ν, the multiplicities of the weights are equal to their multiplicities in an irreducible representation of U(G) with equal highest weight. If the highest weight is dominant and integral (a weight μ is dominant and integral if μ satisfies the condition that is a non-negative integer for all i), then the weight spectrum of the irreducible representation is invariant under the Weyl group for G, and the representation is integrable.
Conversely, if a highest weight module is integrable, then its highest weight vector v satisfies , where cλ · v = dλv are complex numbers such that
for all weights λ and μ,
for all i,
and ν is dominant and integral.
As is the case for all Hopf algebras, the tensor product of two modules is another module. For an element x of Uq(G), and for vectors v and w in the respective modules, x ⋅ (v ⊗ w) = Δ(x) ⋅ (v ⊗ w), so that , and in the case of coproduct Δ1, and
The integrable highest weight module described above is a tensor product of a one-dimensional module (on which kλ = cλ for all λ, and ei = fi = 0 for all i) and a highest weight module generated by a nonzero vector v0, subject to for all weights λ, and for all i.
In the specific case where G is a finite-dimensional Lie algebra (as a special case of a Kac–Moody algebra), then the irreducible representations with dominant integral highest weights are also finite-dimensional.
In the case of a tensor product of highest weight modules, its decomposition into submodules is the same as for the tensor product of the corresponding modules of the Kac–Moody algebra (the highest weights are the same, as are their multiplicities).
Case 2: q is a root of unity
Quasitriangularity
Case 1: q is not a root of unity
Strictly, the quantum group Uq(G) is not quasitriangular, but it can be thought of as being "nearly quasitriangular" in that there exists an infinite formal sum which plays the role of an R-matrix. This infinite formal sum is expressible in terms of generators ei and fi, and Cartan generators tλ, where kλ is formally identified with qtλ. The infinite formal sum is the product of two factors,
and an infinite formal sum, where λj is a basis for the dual space to the Cartan subalgebra, and μj is the dual basis, and η = ±1.
The formal infinite sum which plays the part of the R-matrix has a well-defined action on the tensor product of two irreducible highest weight modules, and also on the tensor product of two lowest weight modules. Specifically, if v has weight α and w has weight β, then
and the fact that the modules are both highest weight modules or both lowest weight modules reduces the action of the other factor on v ⊗ W to a finite sum.
Specifically, if V is a highest weight module, then the formal infinite sum, R, has a well-defined, and invertible, action on V ⊗ V, and this value of R (as an element of End(V ⊗ V)) satisfies the Yang–Baxter equation, and therefore allows us to determine a representation of the braid group, and to define quasi-invariants for knots, links and braids.
Case 2: q is a root of unity
Quantum groups at q = 0
Masaki Kashiwara has researched the limiting behaviour of quantum groups as q → 0, and found a particularly well behaved base called a crystal base.
Description and classification by root-systems and Dynkin diagrams
There has been considerable progress in describing finite quotients of quantum groups such as the above Uq(g) for qn = 1; one usually considers the class of pointed Hopf algebras, meaning that all simple left or right comodules are 1-dimensional and thus the sum of all its simple subcoalgebras forms a group algebra called the coradical:
In 2002 H.-J. Schneider and N. Andruskiewitsch finished their classification of pointed Hopf algebras with an abelian co-radical group (excluding primes 2, 3, 5, 7), especially as the above finite quotients of Uq(g) decompose into E′s (Borel part), dual F′s and K′s (Cartan algebra) just like ordinary Semisimple Lie algebras:
Here, as in the classical theory V is a braided vector space of dimension n spanned by the E′s, and σ (a so-called cocycle twist) creates the nontrivial linking between E′s and F′s. Note that in contrast to classical theory, more than two linked components may appear. The role of the quantum Borel algebra is taken by a Nichols algebra of the braided vectorspace.
A crucial ingredient was I. Heckenberger's classification of finite Nichols algebras for abelian groups in terms of generalized Dynkin diagrams. When small primes are present, some exotic examples, such as a triangle, occur (see also the Figure of a rank 3 Dynkin diagram).
Meanwhile, Schneider and Heckenberger have generally proven the existence of an arithmetic root system also in the nonabelian case, generating a PBW basis as proven by Kharcheko in the abelian case (without the assumption on finite dimension). This can be used on specific cases Uq(g) and explains e.g. the numerical coincidence between certain coideal subalgebras of these quantum groups and the order of the Weyl group of the Lie algebra g.
Compact matrix quantum groups
S. L. Woronowicz introduced compact matrix quantum groups. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry.
The continuous complex-valued functions on a compact Hausdorff topological space form a commutative C*-algebra. By the Gelfand theorem, a commutative C*-algebra is isomorphic to the C*-algebra of continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C*-algebra up to homeomorphism.
For a compact topological group, G, there exists a C*-algebra homomorphism Δ: C(G) → C(G) ⊗ C(G) (where C(G) ⊗ C(G) is the C*-algebra tensor product - the completion of the algebraic tensor product of C(G) and C(G)), such that Δ(f)(x, y) = f(xy) for all f ∈ C(G), and for all x, y ∈ G (where (f ⊗ g)(x, y) = f(x)g(y) for all f, g ∈ C(G) and all x, y ∈ G). There also exists a linear multiplicative mapping κ: C(G) → C(G), such that κ(f)(x) = f(x−1) for all f ∈ C(G) and all x ∈ G. Strictly, this does not make C(G) a Hopf algebra, unless G is finite. On the other hand, a finite-dimensional representation of G can be used to generate a *-subalgebra of C(G) which is also a Hopf *-algebra. Specifically, if is an n-dimensional representation of G, then for all i, j uij ∈ C(G) and
It follows that the *-algebra generated by uij for all i, j and κ(uij) for all i, j is a Hopf *-algebra: the counit is determined by ε(uij) = δij for all i, j (where δij is the Kronecker delta), the antipode is κ, and the unit is given by
General definition
As a generalization, a compact matrix quantum group is defined as a pair (C, u), where C is a C*-algebra and is a matrix with entries in C such that
The *-subalgebra, C0, of C, which is generated by the matrix elements of u, is dense in C;
There exists a C*-algebra homomorphism called the comultiplication Δ: C → C ⊗ C (where C ⊗ C is the C*-algebra tensor product - the completion of the algebraic tensor product of C and C) such that for all i, j we have:
There exists a linear antimultiplicative map κ: C0 → C0 (the coinverse) such that κ(κ(v*)*) = v for all v ∈ C0 and
where I is the identity element of C. Since κ is antimultiplicative, then κ(vw) = κ(w) κ(v) for all v, w in C0.
As a consequence of continuity, the comultiplication on C is coassociative.
In general, C is not a bialgebra, and C0 is a Hopf *-algebra.
Informally, C can be regarded as the *-algebra of continuous complex-valued functions over the compact matrix quantum group, and u can be regarded as a finite-dimensional representation of the compact matrix quantum group.
Representations
A representation of the compact matrix quantum group is given by a corepresentation of the Hopf *-algebra (a corepresentation of a counital coassociative coalgebra A is a square matrix with entries in A (so v belongs to M(n, A)) such that
for all i, j and ε(vij) = δij for all i, j). Furthermore, a representation v, is called unitary if the matrix for v is unitary (or equivalently, if κ(vij) = v*ij for all i, j).
Example
An example of a compact matrix quantum group is SUμ(2), where the parameter μ is a positive real number. So SUμ(2) = (C(SUμ(2)), u), where C(SUμ(2)) is the C*-algebra generated by α and γ, subject to
and
so that the comultiplication is determined by ∆(α) = α ⊗ α − γ ⊗ γ*, ∆(γ) = α ⊗ γ + γ ⊗ α*, and the coinverse is determined by κ(α) = α*, κ(γ) = −μ−1γ, κ(γ*) = −μγ*, κ(α*) = α. Note that u is a representation, but not a unitary representation. u is equivalent to the unitary representation
Equivalently, SUμ(2) = (C(SUμ(2)), w), where C(SUμ(2)) is the C*-algebra generated by α and β, subject to
and
so that the comultiplication is determined by ∆(α) = α ⊗ α − μβ ⊗ β*, Δ(β) = α ⊗ β + β ⊗ α*, and the coinverse is determined by κ(α) = α*, κ(β) = −μ−1β, κ(β*) = −μβ*, κ(α*) = α. Note that w is a unitary representation. The realizations can be identified by equating .
When μ = 1, then SUμ(2) is equal to the algebra C(SU(2)) of functions on the concrete compact group SU(2).
Bicrossproduct quantum groups
Whereas compact matrix pseudogroups are typically versions of Drinfeld-Jimbo quantum groups in a dual function algebra formulation, with additional structure, the bicrossproduct ones are a distinct second family of quantum groups of increasing importance as deformations of solvable rather than semisimple Lie groups. They are associated to Lie splittings of Lie algebras or local factorisations of Lie groups and can be viewed as the cross product or Mackey quantisation of one of the factors acting on the other for the algebra and a similar story for the coproduct Δ with the second factor acting back on the first.
The very simplest nontrivial example corresponds to two copies of R locally acting on each other and results in a quantum group (given here in an algebraic form) with generators p, K, K−1, say, and coproduct
where h is the deformation parameter.
This quantum group was linked to a toy model of Planck scale physics implementing Born reciprocity when viewed as a deformation of the Heisenberg algebra of quantum mechanics. Also, starting with any compact real form of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra (the Iwasawa decomposition), and this provides a canonical bicrossproduct quantum group associated to g. For su(2) one obtains a quantum group deformation of the Euclidean group E(3) of motions in 3 dimensions.
See also
Hopf algebra
Lie bialgebra
Poisson–Lie group
Quantum affine algebra
Notes
References
Mathematical quantization | Quantum group | [
"Physics"
] | 4,476 | [
"Mathematical quantization",
"Quantum mechanics"
] |
340,757 | https://en.wikipedia.org/wiki/Internal%20energy | The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. The internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics. The notion has been introduced to describe the systems characterized by temperature variations, temperature being added to the set of state parameters, the position variables known in mechanics (and their conjugated generalized force parameters), in a similar way to potential energy of the conservative fields of force, gravitational and electrostatic. Its author is Rudolf Clausius. Internal energy changes equal the algebraic sum of the heat transferred and the work done. In systems without temperature changes, potential energy changes equal the work done by/on the system.
The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of substance, or of energy, as heat, or by thermodynamic work. These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property.
Thermodynamics defines internal energy macroscopically, for the body as a whole. In statistical mechanics, the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energies associated with microscopic forces, including chemical bonds.
The unit of energy in the International System of Units (SI) is the joule (J). The internal energy relative to the mass with unit J/kg is the specific internal energy. The corresponding quantity relative to the amount of substance with unit J/mol is the molar internal energy.
Cardinal functions
The internal energy of a system depends on its entropy S, its volume V and its number of massive particles: . It expresses the thermodynamics of a system in the energy representation. As a function of state, its arguments are exclusively extensive variables of state. Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy, as a function, , of the same list of extensive variables of state, except that the entropy, , is replaced in the list by the internal energy, . It expresses the entropy representation.
Each cardinal function is a monotonic function of each of its natural or canonical variables. Each provides its characteristic or fundamental equation, for example , that by itself contains all thermodynamic information about the system. The fundamental equations for the two cardinal functions can in principle be interconverted by solving, for example, for , to get .
In contrast, Legendre transformations are necessary to derive fundamental equations for other thermodynamic potentials and Massieu functions. The entropy as a function only of extensive state variables is the one and only cardinal function of state for the generation of Massieu functions. It is not itself customarily designated a 'Massieu function', though rationally it might be thought of as such, corresponding to the term 'thermodynamic potential', which includes the internal energy.
For real and practical systems, explicit expressions of the fundamental equations are almost always unavailable, but the functional relations exist in principle. Formal, in principle, manipulations of them are valuable for the understanding of thermodynamics.
Description and definition
The internal energy of a given state of the system is determined relative to that of a standard state of the system, by adding up the macroscopic transfers of energy that accompany a change of state from the reference state to the given state:
where denotes the difference between the internal energy of the given state and that of the reference state,
and the are the various energies transferred to the system in the steps from the reference state to the given state.
It is the energy needed to create the given state of the system from the reference state. From a non-relativistic microscopic point of view, it may be divided into microscopic potential energy, , and microscopic kinetic energy, , components:
The microscopic kinetic energy of a system arises as the sum of the motions of all the system's particles with respect to the center-of-mass frame, whether it be the motion of atoms, molecules, atomic nuclei, electrons, or other particles. The microscopic potential energy algebraic summative components are those of the chemical and nuclear particle bonds, and the physical force fields within the system, such as due to internal induced electric or magnetic dipole moment, as well as the energy of deformation of solids (stress-strain). Usually, the split into microscopic kinetic and potential energies is outside the scope of macroscopic thermodynamics.
Internal energy does not include the energy due to motion or location of a system as a whole. That is to say, it excludes any kinetic or potential energy the body may have because of its motion or location in external gravitational, electrostatic, or electromagnetic fields. It does, however, include the contribution of such a field to the energy due to the coupling of the internal degrees of freedom of the system with the field. In such a case, the field is included in the thermodynamic description of the object in the form of an additional external parameter.
For practical considerations in thermodynamics or engineering, it is rarely necessary, convenient, nor even possible, to consider all energies belonging to the total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Indeed, in most systems under consideration, especially through thermodynamics, it is impossible to calculate the total internal energy. Therefore, a convenient null reference point may be chosen for the internal energy.
The internal energy is an extensive property: it depends on the size of the system, or on the amount of substance it contains.
At any temperature greater than absolute zero, microscopic potential energy and kinetic energy are constantly converted into one another, but the sum remains constant in an isolated system (cf. table). In the classical picture of thermodynamics, kinetic energy vanishes at zero temperature and the internal energy is purely potential energy. However, quantum mechanics has demonstrated that even at zero temperature particles maintain a residual energy of motion, the zero point energy. A system at absolute zero is merely in its quantum-mechanical ground state, the lowest energy state available. At absolute zero a system of given composition has attained its minimum attainable entropy.
The microscopic kinetic energy portion of the internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore, it relates the mean microscopic kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system. While temperature is an intensive measure, this energy expresses the concept as an extensive property of the system, often referred to as the thermal energy, The scaling property between temperature and thermal energy is the entropy change of the system.
Statistical mechanics considers any system to be statistically distributed across an ensemble of microstates. In a system that is in thermodynamic contact equilibrium with a heat reservoir, each microstate has an energy and is associated with a probability . The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by its probability of occurrence:
This is the statistical expression of the law of conservation of energy.
Internal energy changes
Thermodynamics is chiefly concerned with the changes in internal energy .
For a closed system, with mass transfer excluded, the changes in internal energy are due to heat transfer and due to thermodynamic work done by the system on its surroundings. Accordingly, the internal energy change for a process may be written
When a closed system receives energy as heat, this energy increases the internal energy. It is distributed between microscopic kinetic and microscopic potential energies. In general, thermodynamics does not trace this distribution. In an ideal gas all of the extra energy results in a temperature increase, as it is stored solely as microscopic kinetic energy; such heating is said to be sensible.
A second kind of mechanism of change in the internal energy of a closed system changed is in its doing of work on its surroundings. Such work may be simply mechanical, as when the system expands to drive a piston, or, for example, when the system changes its electric polarization so as to drive a change in the electric field in the surroundings.
If the system is not closed, the third mechanism that can increase the internal energy is transfer of substance into the system. This increase, cannot be split into heat and work components. If the system is so set up physically that heat transfer and work that it does are by pathways separate from and independent of matter transfer, then the transfers of energy add to change the internal energy:
If a system undergoes certain phase transformations while being heated, such as melting and vaporization, it may be observed that the temperature of the system does not change until the entire sample has completed the transformation. The energy introduced into the system while the temperature does not change is called latent energy or latent heat, in contrast to sensible heat, which is associated with temperature change.
Internal energy of the ideal gas
Thermodynamics often uses the concept of the ideal gas for teaching purposes, and as an approximation for working systems. The ideal gas consists of particles considered as point objects that interact only by elastic collisions and fill a volume such that their mean free path between collisions is much larger than their diameter. Such systems approximate monatomic gases such as helium and other noble gases. For an ideal gas the kinetic energy consists only of the translational energy of the individual atoms. Monatomic particles do not possess rotational or vibrational degrees of freedom, and are not electronically excited to higher energies except at very high temperatures.
Therefore, the internal energy of an ideal gas depends solely on its temperature (and the number of gas particles): . It is not dependent on other thermodynamic quantities such as pressure or density.
The internal energy of an ideal gas is proportional to its amount of substance (number of moles) and to its temperature
where is the isochoric (at constant volume) molar heat capacity of the gas; is constant for an ideal gas. The internal energy of any gas (ideal or not) may be written as a function of the three extensive properties , , (entropy, volume, number of moles). In case of the ideal gas it is in the following way
where is an arbitrary positive constant and where is the universal gas constant. It is easily seen that is a linearly homogeneous function of the three variables (that is, it is extensive in these variables), and that it is weakly convex. Knowing temperature and pressure to be the derivatives
the ideal gas law immediately follows as below:
Internal energy of a closed thermodynamic system
The above summation of all components of change in internal energy assumes that a positive energy denotes heat added to the system or the negative of work done by the system on its surroundings.
This relationship may be expressed in infinitesimal terms using the differentials of each term, though only the internal energy is an exact differential. For a closed system, with transfers only as heat and work, the change in the internal energy is
expressing the first law of thermodynamics. It may be expressed in terms of other thermodynamic parameters. Each term is composed of an intensive variable (a generalized force) and its conjugate infinitesimal extensive variable (a generalized displacement).
For example, the mechanical work done by the system may be related to the pressure and volume change . The pressure is the intensive generalized force, while the volume change is the extensive generalized displacement:
This defines the direction of work, , to be energy transfer from the working system to the surroundings, indicated by a positive term. Taking the direction of heat transfer to be into the working fluid and assuming a reversible process, the heat is
where denotes the temperature, and denotes the entropy.
The change in internal energy becomes
Changes due to temperature and volume
The expression relating changes in internal energy to changes in temperature and volume is
This is useful if the equation of state is known.
In case of an ideal gas, we can derive that , i.e. the internal energy of an ideal gas can be written as a function that depends only on the temperature.
The expression relating changes in internal energy to changes in temperature and volume is
The equation of state is the ideal gas law
Solve for pressure:
Substitute in to internal energy expression:
Take the derivative of pressure with respect to temperature:
Replace:
And simplify:
To express in terms of and , the term
is substituted in the fundamental thermodynamic relation
This gives
The term is the heat capacity at constant volume
The partial derivative of with respect to can be evaluated if the equation of state is known. From the fundamental thermodynamic relation, it follows that the differential of the Helmholtz free energy is given by
The symmetry of second derivatives of with respect to and yields the Maxwell relation:
This gives the expression above.
Changes due to temperature and pressure
When considering fluids or solids, an expression in terms of the temperature and pressure is usually more useful:
where it is assumed that the heat capacity at constant pressure is related to the heat capacity at constant volume according to
The partial derivative of the pressure with respect to temperature at constant volume can be expressed in terms of the coefficient of thermal expansion
and the isothermal compressibility
by writing
and equating dV to zero and solving for the ratio dP/dT. This gives
Substituting () and () in () gives the above expression.
Changes due to volume at constant temperature
The internal pressure is defined as a partial derivative of the internal energy with respect to the volume at constant temperature:
Internal energy of multi-component systems
In addition to including the entropy and volume terms in the internal energy, a system is often described also in terms of the number of particles or chemical species it contains:
where are the molar amounts of constituents of type in the system. The internal energy is an extensive function of the extensive variables , , and the amounts , the internal energy may be written as a linearly homogeneous function of first degree:
where is a factor describing the growth of the system. The differential internal energy may be written as
which shows (or defines) temperature to be the partial derivative of with respect to entropy and pressure to be the negative of the similar derivative with respect to volume ,
and where the coefficients are the chemical potentials for the components of type in the system. The chemical potentials are defined as the partial derivatives of the internal energy with respect to the variations in composition:
As conjugate variables to the composition , the chemical potentials are intensive properties, intrinsically characteristic of the qualitative nature of the system, and not proportional to its extent. Under conditions of constant and , because of the extensive nature of and its independent variables, using Euler's homogeneous function theorem, the differential may be integrated and yields an expression for the internal energy:
The sum over the composition of the system is the Gibbs free energy:
that arises from changing the composition of the system at constant temperature and pressure. For a single component system, the chemical potential equals the Gibbs energy per amount of substance, i.e. particles or moles according to the original definition of the unit for .
Internal energy in an elastic medium
For an elastic medium the potential energy component of the internal energy has an elastic nature expressed in terms of the stress and strain involved in elastic processes. In Einstein notation for tensors, with summation over repeated indices, for unit volume, the infinitesimal statement is
Euler's theorem yields for the internal energy:
For a linearly elastic material, the stress is related to the strain by
where the are the components of the 4th-rank elastic constant tensor of the medium.
Elastic deformations, such as sound, passing through a body, or other forms of macroscopic internal agitation or turbulent motion create states when the system is not in thermodynamic equilibrium. While such energies of motion continue, they contribute to the total energy of the system; thermodynamic internal energy pertains only when such motions have ceased.
History
James Joule studied the relationship between heat, work, and temperature. He observed that friction in a liquid, such as caused by its agitation with work by a paddle wheel, caused an increase in its temperature, which he described as producing a quantity of heat. Expressed in modern units, he found that c. 4186 joules of energy were needed to raise the temperature of one kilogram of water by one degree Celsius.
Notes
See also
Calorimetry
Enthalpy
Exergy
Thermodynamic equations
Thermodynamic potentials
Gibbs free energy
Helmholtz free energy
References
Bibliography of cited references
Adkins, C. J. (1968/1975). Equilibrium Thermodynamics, second edition, McGraw-Hill, London, .
Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, .
Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London.
Callen, H. B. (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, .
Crawford, F. H. (1963). Heat, Thermodynamics, and Statistical Physics, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc.
Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081.
.
Münster, A. (1970), Classical Thermodynamics, translated by E. S. Halberstadt, Wiley–Interscience, London, .
Planck, M., (1923/1927). Treatise on Thermodynamics, translated by A. Ogg, third English edition, Longmans, Green and Co., London.
Tschoegl, N. W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, .
Bibliography
Physical quantities
Thermodynamic properties
State functions
Statistical mechanics
Energy (physics) | Internal energy | [
"Physics",
"Chemistry",
"Mathematics"
] | 4,022 | [
"State functions",
"Physical phenomena",
"Thermodynamic properties",
"Physical quantities",
"Quantity",
"Statistical mechanics",
"Energy (physics)",
"Thermodynamics",
"Wikipedia categories named after physical quantities",
"Physical properties"
] |
340,760 | https://en.wikipedia.org/wiki/Discussion%20group | A discussion group is a group of individuals, typically who share a similar interest, who gather either formally or informally to discuss ideas, solve problems, or make comments. Common methods of conversing including meeting in person, conducting conference calls, using text messaging, or using a website such as an Internet forum. People respond, add comments, and make posts on such forums, as well as on established mailing lists, in news groups, or in IRC channels. Other group members could choose to respond by posting text or image.
Brief history
Discussion group was evolved from USENET which is a traced back to early 80's. Two computer scientists Jim Ellis and Tom Truscott founded the idea of setting a system of rules to produce "articles", and then send back to their parallel news group. Fundamentally, the form of discussion group was generated on the concept of USENET, which emphasised ways of communication via email and web forums. Gradually, USENET had developed to be a system of channels which provide notifications and "articles" to meet general public's needs. Nowadays, World Wide Web gradually takes on the major role of supporting and extending platforms for discussion group on the Internet by setting up various web servers.
Small-Group Discussions
Small-Group Discussions, consisting of a minimum of three and maximum of about 20 people, have been found to be more effective in medical teaching.
Overview of popular online discussion group systems
Google Groups
Google Groups has become one of the major online discussion groups, with a wide range of worldwide frequent users. Features include:
the ability for anyone to create new groups and join existing groups.
the ability to search for groups that focus on specific subject matter, as well as advanced search features that allow the search results to be filtered by date, language, and post author, among others.
three levels of group participation: public, announcements only, and restricted.
Facebook groups
Facebook groups simplify processes and protect the privacy of users when they interact with people. Users can create a group and delegate admins. Group admins are able to make a range of adjustments to the group page, such as changing its cover photo, moderating posts and comments, and pinning posts so that they permanently appear at the top of the group page. Admins can also create group events, news updates and manage group members. By default, groups are public, and anyone can join them at the discretion of that group's admins. However, groups may be marked as private — a user may only join such a group if an existing member sends them an invitation. A single user is capable of joining a maximum of 6000 groups.
WhatsApp groups
WhatsApp is a mobile messaging app with group discussion features. Users can create group chats to facilitate group discussions. By default, all group members are admins of that group, but this may be changed at the discretion of any existing admin. Admins have the ability to rename the group, add and remove members, and delete messages that have been sent to the group.
Advantages
Advantages: the implementation of Google Groups comes with its own advantages. For diverse users, it provides the service of interpreting languages widely, which helps present a better way to communicate effectively with people in different countries. Considering of storage, one group member enjoys "100 megabytes (MB)" while there are no restrictions for the whole group. It delivers convenience for group members work on projects that need considerably more storage than normal files, for example, presentations. Studies conducted by Kushin and Kitchener indicates Facebook provide users in discussion groups with more opportunities to post content that has correlation with "social, political, or sporting issues". For WhatsApp users, the communication service brings enjoyment to share ideas with comparatively low cost. Ideally, it enhanced the quality of communication regarding of its records saving, security and trustability.
Information in Discussion groups are usually archived. For example, Google's Groups (formerly DejaNews) is an archive of Usenet articles trace back to 1981. Discussion group archives are sometimes an effective way to find an answer to very ambiguous questions.
Academic
Small group of professionals or students formally or informally negotiate about an academic topic within certain fields. This implementation could be seen as an investigation or research based on various academic levels. For instance, "one hundred eighty college-level psychology students" breakdown into different groups to participate in giving an orderly arrangement of preferred events. Nevertheless, discussion groups could support professional services and hold events to a range of demographics; another distinguished example is from "The London Biological Mass Spectrometry Discussion Group", which sustainably operates by gathering "technicians, clinicians, academics, industrialists and students" to exchange ideas on an academic level. It attributes to the development of participants' cognitive, critical thinking, and analytical skills.
See also
Bulletin board system
Chat room
E learning
Internet forum
Social network
User group
References
Further reading
Bliuc, A., Ellis, R., Goodyear, P. and Piggott, L. (2011). A blended learning Approach to teaching foreign policy: Student experiences of learning through face-to-face and online discussion and their relationship to academic performance. Computers \& Education, 56(3), pp. 856–864.
Hanna, B. and De Nooy, J. (2009). Learning language and culture via public internet discussion forums. Palgrave Macmillan.
Omar, H., Embi, M. and Yunus, M. (2012). Learners' use of communication strategies in an online discussion via Facebook. Procedia - Social and Behavioral Sciences, 64, pp. 535–544.
Vicente, M., Fern\'andez, C., \~Neco, R. and Puerto, R. (2010). GOOGLE GROUPS FOR COMMUNICATION ENHANCEMENT IN COOPERATIVE LEARNING STRATEGIES. EDULEARN10 Proceedings, pp. 1031–1036.
Human communication | Discussion group | [
"Biology"
] | 1,203 | [
"Human communication",
"Behavior",
"Human behavior"
] |
340,774 | https://en.wikipedia.org/wiki/Steve%20Urkel | Steven Quincy Urkel is a fictional character on the American ABC/CBS sitcom Family Matters, portrayed by Jaleel White. Originally slated for a single appearance, he broke out to be the show's most popular character, gradually becoming its protagonist. Due to the character's off-putting characteristics, a tendency to stir up events, and his role in the show's plotlines, he is considered a nuisance by the original protagonist's family, the Winslows. However, they come to accept him over time.
The character epitomizes a geek or nerd of the era, with large, thick eyeglasses, flood pants held up by suspenders, bad posture, multi-colored cardigan sweaters, saddle shoes, and a high-pitched voice. He professes love for his neighbor Laura Winslow. This love often leads to mishaps that trigger plot points and crises, and is unrequited until the series' end.
Throughout the series, Urkel is central to many of its running gags, primarily property damage and personal injury resulting from his inventions going awry or his clumsiness. The character became associated with catchphrases including "I've fallen and I can't get up!", "I don't have to take this. I'm going home.", "Did I do that?", "Whoa, Mama!", and "Look what you did!"
Character development
Steve Urkel first appeared in the show's twelfth episode, "Laura's First Date", where he is introduced as a nerdy young boy who takes Laura Winslow out on a date. Despite him being madly in love with her, Laura finds Steve grating and doesn't return his affection. While initially intended to be a minor character, Urkel became very popular with audiences for his oddball antics, and became a recurring character. To naturally introduce the character to audiences upon repeated viewings, the creators added a scene with Steve to the show's fourth episode "Rachel's First Date", which became his first appearance in syndication. Steve joined the main cast beginning with the season-two premiere "Rachel's Place".
Family Matters co-creator Michael Warren named the character after his friend, writer and director Steve Erkel. Due to the show and the character's tremendous popularity during the early 1990s, Erkel encountered difficulties using his own name. He received many prank phone calls from "Laura" asking for "Steve", and businesses found his name to be suspicious. Warren stated that had he known the character would reappear for years, he would not have named him after his friend.
Portrayal
Steve Urkel embodies the stereotype of a socially inept intellectual who means well but often messes things up. Despite his intelligence, his actions often come across as clumsy and foolish. He is fiercely protective of and obsessed with Laura Winslow, and this admiration extends to the rest of the Winslow family. His attempts to help the Winslows often go awry. This puts him at odds with the family patriarch, Carl, who routinely throws Urkel out of his house. He has been shown to take responsibility for his own mistakes and reimburses the Winslows for damage he's caused. Steve is close to Harriette Winslow, who is delighted when he comes over, much to Carl's chagrin.
Later episodes suggest that Steve's attachment to the Winslows stems from his bad relationship with his own family. Urkel often hints that most of his relatives, including his (never seen) parents, despise him and refuse to associate with him. This culminates in the two moving to Russia without him, and Urkel moving in with the Winslows. The show's plots reveal that Steve has at least four relatives who care about him. They are Uncle Ernie, Uncle Cecil (who, despite his gambling problems, visits the Urkel home to keep an eye on him), Aunt Oona from Altoona (played by singer Donna Summer), who is like a mother to him, and cousin Myrtle. In the series finale, Steve is non-bothered when he tells Laura that his parents won't be able to attend their wedding because their favorite episode of The Mod Squad will be airing in Russia, and later responds to Carl talking about how proud he is of his future son-in-law by saying "Thanks, Dad."
Urkel dresses unfashionably and is most commonly seen wearing suspenders, brightly colored shirts, and high-water pants. His hobbies include polka dancing and accordion playing. His motor vehicle of choice is the small three-wheeled Isetta. Unlike his friends, he is not interested in popular culture or sports, though he enjoys playing basketball and attempts to join the school team. This causes Myra to be attracted to Urkel but he shows little interest in her, mainly due to her stalker behavior.
While he is unpopular with his schoolmates, Urkel is a brilliant student and is on a first-name basis with his teachers. He is a genius inventor, and his fantastical but unreliable gadgets (including a transformation device and a time machine) are central to many Family Matters plots and gags, especially during later seasons.
Urkel sometimes breaks the law as a result of peer pressure. He is depicted learning the consequences when finding himself in situations outside of his control.
Stefan Urquelle
During the season five episode "Dr. Urkel and Mr. Cool", Urkel devises a plan to win Laura's heart. In a spoof of the original Nutty Professor film, he transforms his DNA using a serum, suppressing his "nerd genes" and bringing out his "cool genes". This creates the alter ego Stefan Urquelle, also played by Jaleel White in more stylish attire. Initially, Laura is enamored with the smoother Stefan, but she asks that he turn back into Steve when Stefan's self-centeredness becomes apparent.
Steve improves the formula in the season five episode "Stefan Returns". He reduces its negative effects on his personality and invents a "transformation chamber", allowing him to become Stefan at will. He changes into Stefan several times – even while dating Myra – but circumstances force Steve to turn into his normal self again. With his narcissistic tendencies toned down, Laura falls deeply in love with Steve's alter-ego. A major factor in creating and extensively utilizing Stefan was the simple fact that doing the distinctive voice of Steve Urkel was starting to cause damage to Jaleel White's throat, so having him play a character who could speak in a normal voice gave him time to recover (White could still sound like Steve, but with less weight on that he was able to avoid any long-term issues).
In the seventh-season finale "Send in the Clones", Steve creates a cloning machine and winds up creating a perfect duplicate of himself. Myra is initially excited, but eventually realizes that two Steves are too much. Laura proposes that one of the Steves be permanently turned into Stefan, so that she and Myra can both be with the one they love. Stefan becomes a recurring character and eventually proposes to Laura in the ninth season. After weighing her choices in the episode "Pop Goes the Question", Laura chooses Steve over Stefan. Stefan leaves and does not appear again.
Cultural impact
In 2010, Westside Middle School in Memphis, Tennessee, outlined its dress code policy on sagging pants, asking students to pull them up or get "Urkeled". Teachers would forcibly pull students' pants up and attach them to their waist using zip ties. Students would also have their photo taken and posted on a board in the hallway so that it would be visible to all their classmates. In an interview with NBC affiliate WMC-TV, Principal Bobby White stated that the general idea is to fight pop culture with pop culture. One teacher at the school claimed to have "Urkeled" up to 80 students per week, although after five weeks, the number dropped to 18.
Ratings effect
In syndication, Steve is incorporated into the teaser scene of "Rachel's First Date". His first appearance in the original broadcasts is in the 1989 episode "Laura's First Date". In the episode, Carl and Eddie separately set up dates for Laura for a dance or party. The first thing known about Steve is that he allegedly ate a mouse. He later makes reference to a mouse when speaking to Carl, implying that it might be true. Prior to Steve Urkel's introduction, the show was at risk of cancellation due to mediocre ratings. After Urkel was introduced, several scripts had to be hastily rewritten to accommodate the character, while several first-season episodes that had been completed had new opening gag sequences filmed featuring Steve trying to push open the Winslows' front door while the family holds it shut. The addition of Steve immediately helped the show boost its modest ratings. White was credited as a guest star in the first season and became a regular member of the cast in season two. In the opening credits for seasons five to nine, White was the only regular whose character's name appeared alongside his own during the opening credits. Season nine did not have the same credit sequence showing all the actors, it simply listed their names across the bottom of the screen, but White was listed "as Steve Urkel" there as well.
Jo Marie Payton, who played Harriette Winslow, admitted that she felt the Urkel character hogged much of the show's attention and disrupted the close family relationship she had formed with the rest of the cast. Payton took particular umbrage when Jaimee Foxworth, who played youngest sibling Judy Winslow, was dismissed to make more room for Urkel plotlines. Payton felt particularly close to Foxworth, who was the baby of the cast. Payton experienced increasing burnout over the course of the show because the production staff gave White free rein to misbehave. She felt that the focus on Urkel had made the show jump the shark. She almost quit when the show moved to CBS but agreed to stay for the first several episodes until the role of Harriette was recast. Payton was replaced by Judyann Elder. In an interview with Entertainment Tonight, Payton recalled an instance in which White insisted upon inserting something that would have violated Broadcast Standards and Practices, to the point that he and Payton nearly came to physical blows with each other. White is one of the few living members of the cast with whom Payton no longer speaks regularly. Still, she speaks well of her experiences, appreciating Urkel's impact on the show's popularity and the resulting residuals. Reginald VelJohnson, in a 2022 interview with Entertainment Tonight, acknowledged that White could be difficult to work with. He attributed the difficulties to White's young age and being surrounded by other teenagers, which VelJohnson (who himself never had children) found overwhelming. On the whole, VelJohnson had "nothing but good memories" of working with White.
The Urkel Dance
The Urkel Dance was a novelty dance that originated in the season two episode, "Life of the Party". It incorporated Urkel's hitched-up pants and nasal voice. The dance was popular enough to appear on another show, Step by Step, when the Steve Urkel character appeared in a crossover in the season one episode, "The Dance".
Jaleel White also performed the song in character during the 5th Annual American Comedy Awards. Bea Arthur (from Maude & The Golden Girls) joined him on stage to "Do The Urkel", after which she said, "Hey, MC Hammer, try and touch that!"
A promotional cassette single of the song that accompanies the dance was produced and distributed in limited numbers. A T-shirt was also produced featuring lyrics and Urkel's likeness.
Rick Sanchez pays homage to The Urkel Dance with "The Rick Dance" in the Rick and Morty episode "Ricksy Business".
Appearances on other shows
Full House – In the 1991 episode, "Stephanie Gets Framed", Steve is called in to help Stephanie Tanner (Jodie Sweetin) deal with her anxieties after she has to get glasses. He was cousin to a friend of D.J. He also jams with Uncle Jesse and gives Michelle a penny for her piggy bank, telling her that "with prevailing interest rates, that penny will be worth three cents by the turn of the century". Incidentally, Family Matters did not air on the night of the episode's original airdate (January 25, 1991). It is implied that he found himself in San Francisco in the Full House universe before paying a visit to the Lambert household from Step by Step.
Step by Step – In the series' second episode, "The Dance", Steve lands in the Lambert-Foster family's backyard after launching himself with a rocket pack from the living room of the Winslows' house in the Family Matters episode "Brain Over Brawn". The two scenes were shown in uninterrupted sequence, as Family Matters and Step by Step aired back to back on ABC's TGIF lineup. Urkel then helps his science-fair pen pal, Mark Foster (Christopher Castile), and lifts Alicia "Al" Lambert (Christine Lakin)'s spirits after her potential date dumps her just before a school dance. White reprises his "Do the Urkel" dance in the scene where Al gives the boy that dumped her his comeuppance. White also makes a brief two-second cameo as Steve in the 1997 episode "A Star Is Born", snapping a clapperboard on the set of the movie that Al was cast in over her two sisters.
In the Family Matters episode "Beauty and the Beast", Steve sends a chain letter to his friend Cory Matthews, who lived in Philadelphia. The reference is to Ben Savage's character from Boy Meets World, but there were no on-screen crossovers. In an episode of Boy Meets World, Cory says he receives a chain letter from his friend Steve. (In the sequel series Girl Meets World, though Urkel never appears, an unnamed Carl Winslow-like police officer, portrayed by VelJohnson, does.)
Fuller House - In the Season 3 finale, Urkel was mentioned by D.J.. In a January 2018 interview with TVLine's Andy Swift, series creator and former show runner Jeff Franklin mentioned that they have talked about White reprising the role and that they had some ideas for the character if White decides to reprise the role (Franklin was dismissed from the show before this materialized, and Urkel never appeared in the series).
Scooby-Doo and Guess Who? - White reprised his role on the animated series Scooby-Doo and Guess Who? in the episode "When Urkel-Bots Go Bad!"
Urkel Saves Santa: The Movie - White reprised his role in an original animated Christmas movie
Urkel would play a lead role in a sketch mocking the increasingly ridiculous plots of the later seasons of Family Matters in the series Key & Peele (specifically in the season 4 episode "Slap-Ass: In Recovery"); in the sketch, Reginald VelJohnson and an ABC executive named only "Gene" are seen having an intense argument off-set over the outlandish plots and the obsessive reliance on Urkel; it is suddenly interrupted when Gene stopped mid-sentence, declared he was "nothing", then pulled out and loaded a handgun, further declared "the king is dead... long live the king", and shot himself in the head. Urkel, portrayed by Tyler James Williams, is then revealed to have forced Gene to shoot himself using telekinetic powers, and despite VelJohnson attempting to defend himself with Gene's gun (which fails as Gene had only loaded one bullet), uses such powers to force VelJohnson to point the gun at himself, only stopping him when he agrees to not complain and simply perform the sketches.
Merchandise
At the height of his popularity in 1991, several Urkel-branded products were released. They included a short-lived fruit-flavored cereal, Urkel-Os, and a Steve Urkel pull-string doll. A T-shirt line was created in 2002 but was discontinued shortly after its inception.
In 2021, White launched his own cannabis brand featuring a strain called "Purple Urkel". He reprised the Urkel role in a promotional skit with Snoop Dogg.
Reception
In 1999, TV Guide ranked Urkel #27 on its list of the "50 Greatest TV Characters of All Time". In 2004, he was listed at #98 in Bravo's 100 Greatest TV Characters.
Notes
American male characters in sitcoms
Family Matters
African-American characters in television
Fictional biochemists
Fictional characters from Chicago
Fictional characters with alter egos
Fictional clones
Fictional geneticists
Fictional inventors
Fictional mechanical engineers
Fictional models
Fictional musicians
Fictional NASA astronauts
Teenage characters in television
Television characters introduced in 1989
Time travelers | Steve Urkel | [
"Chemistry"
] | 3,510 | [
"Fictional biochemists",
"Biochemists"
] |
340,782 | https://en.wikipedia.org/wiki/Pykrete | Pykrete (, ) is a frozen ice composite, originally made of approximately 14% sawdust or some other form of wood pulp (such as paper) and 86% ice by weight (6 to 1 by weight).
During World War II, Geoffrey Pyke proposed it as a candidate material for a supersized aircraft carrier for the British Royal Navy. Pykrete features unusual properties, including a relatively slow melting rate due to its low thermal conductivity, as well as a vastly improved strength and toughness compared to ordinary ice. These physical properties can make the material comparable to concrete, as long as the material is kept frozen.
Pykrete is slightly more difficult to form than concrete, as it expands during the freezing process. However, it can be repaired and maintained using seawater as a raw material. The mixture can be moulded into any shape and frozen, and it will be tough and durable, as long as it is kept at or below freezing temperature. Resistance to gradual creep or sagging is improved by lowering the temperature further, to .
History
During World War II
Geoffrey Pyke managed to convince Lord Mountbatten of the potential of his proposal (actually prior to the invention of pykrete) sometime around 1942, and trials were made at two locations in Alberta, Canada. The idea for a ship made of ice impressed the United States and Canada enough that a , 1,000-ton ship was built in one month on Patricia Lake in the Canadian Rockies. However, it was constructed using plain ice (from the lake), before pykrete was proposed. It took slightly more than an entire summer to melt, but plain ice proved to be too weak. Pyke learned from a report by Herman Mark and his assistant that ice made from water mixed with wood fibres formed a strong solid mass—much stronger than pure water ice. Max Perutz later recalled:
Perutz would later learn that Project Habakkuk was the plan to build an enormous aircraft carrier, actually more of a floating island than a ship in the traditional sense. The experiments of Perutz and his collaborators in Smithfield Meat Market in the City of London took place in great secrecy behind a screen of animal carcasses. The tests confirmed that pykrete is much stronger than pure ice and does not shatter, but also that it sags under its own weight at temperatures higher than .
Mountbatten's reaction to the breakthrough is recorded by Pyke's biographer David Lampe:
Another tale is that at the Quebec Conference of 1943, Mountbatten brought a block of pykrete along to demonstrate its potential to the entourage of admirals and generals who had come along with Winston Churchill and Franklin D. Roosevelt. Mountbatten entered the project meeting with two blocks and placed them on the ground. One was a normal ice block and the other was pykrete. He then drew his service pistol and shot at the first block. It shattered and splintered. Next, he fired at the pykrete to give an idea of the resistance of that kind of ice to projectiles. The bullet ricocheted off the block, grazing the trouser leg of Admiral Ernest King and ending up in the wall. According to Perutz's own account, however, the incident of a ricochetting bullet hitting an Admiral actually happened much earlier in London and the gun was fired by someone on the project—not Mountbatten.
Despite these tests, the main Project Habakkuk was never put into action because of limitations in funds and the belief that the tides of the war were beginning to turn in favour of the Allies using more conventional methods.
According to the memoirs of British General Ismay:
After World War II
Since World War II, pykrete has remained a scientific curiosity, unexploited by research or construction of any significance. However, new concepts for pykrete crop up occasionally among architects, engineers and futurists, usually regarding its potential for mammoth offshore construction or its improvement by applying super-strong materials such as synthetic composites or Kevlar.
In 1985, pykrete was considered for a quay in Oslo harbour. However, the idea was later shelved, considering pykrete's unreliability in the real-world environment. Since pykrete needs to be preserved at or below freezing point, and tends to sag under its own weight at temperatures above , an alternative was considered that would guarantee effectiveness and public safety.
In 2011, the Vienna University of Technology successfully built a pykrete ice dome, measuring in diameter in the Austrian village of Obergurgl. They improved on an original Japanese technique of spraying ice on a balloon by using the natural properties of ice and its strength. This structure managed to stand for three months before sunlight started melting the ice, rendering the structure unreliable. Researcher Johann Kollegger of Vienna University of Technology thinks his team's alternative new method is easier, avoiding icy sprayback onto the workers. To build their freestanding structure, Kollegger and his colleagues first cut an plate of ice into 16 segments. To sculpt the segments to have a dome-like curve, the researchers relied on ice's creep behavior. If pressure is applied to ice, it slowly changes its shape without breaking. One of the mechanisms by which glaciers move, called glacial creep, functions similarly, the researchers say.
In 2014, the Eindhoven University of Technology worked on a pykrete architecture project in Juuka, Finland, which included an ice dome and a pykrete scale model of the Sagrada Familia. They attempted to build the largest ice dome in the world. Due to human error, the plug to a compressor that kept the balloon inflated was pulled, leading to the balloon deflating. The team of Dutch students quickly re-inflated the balloon, and resprayed the part of the dome that had collapsed. They continued with their construction, and eventually opened the dome to the public. However within a matter of days the roof caved in; there were no visitors on the site at the time.
Mechanical properties
The durability of pykrete is still debated. Perutz has estimated a crushing strength value of around .
A September 1943 proposal for making smaller pykrete vessels included the following table of characteristics:
In the media
In 2009, the Discovery Channel program MythBusters episode 115 tested the properties of pykrete and the myths behind it. First, the program's primary hosts, Adam Savage and Jamie Hyneman, compared the mechanical properties of common ice, pykrete, and a new material specially created for the show, dubbed "super pykrete", which used newspapers instead of woodpulp. Both versions of pykrete indeed proved to be much stronger than the chunk of ice, withstanding hundreds of pounds of weight. The super pykrete was much stronger than the original version.
The MythBusters then built a full-size boat out of the super pykrete, naming it Yesterday's News, and subjected it to real-world conditions. The MythBusters vessel did not contain refrigeration units to keep the pykrete frozen as the original plans called for, and the boat had a much thinner construction than the massive ships proposed in World War II. Though the boat managed to float and stay intact at speeds of up to , it quickly began to spring leaks as the boat slowly melted. After 20 minutes the boat was deteriorating, and the experiment was ended. The boat lasted another 10 minutes while being piloted back to shore. Though the boat worked, it was noted that it would be highly impractical for the original proposal, which claimed that an entire aircraft carrier could be built out of pykrete. Their conclusion was "Plausible, but ludicrous", since it would involve building vessels out of tens of thousands of tons of the material that would sink without being kept cool.
In the same year, the story of Pyke and pykrete in the Second World War also played an important role in Giles Foden's book Turbulence, about a (fictitional) British meteorologist and his contributions to D-Day weather forecasting. The main character is also involved in the post-War pykrete effort.
In 2010, the BBC programme Bang Goes the Theory episode 26 tested a , 5-tonne pykrete boat made with hemp rather than wood pulp. All four presenters, Jem Stansfield, Dallas Campbell, Liz Bonnin, and Yan Wong, had to be rescued from Portsmouth Harbour after the boat took on water through the engine mounts. It eventually capsized after melting much faster than anticipated in the warmer-than-expected September waters.
2013 German TV station WDR's programme experimented with pykrete but replaced the woodpulp by hemp-fibres. A 5 cm (2.1 inch)-thick plate withstood even more than 80 kg without breaking, it only started to bend.
Neal Stephenson's 2015 novel Seveneves describes the fictional use of pykrete to construct low Earth orbit habitats and spaceship hulls.
99% Invisible's third volume of mini-stories podcasts includes an article about Project Habbakuk and the creation, proposal, and eventual scrapping of pykrete as a useful building material during WWII.
Science & Futurism with Isaac Arthur Youtube episode "Colonizing Ceres" describes the fictional use of pykrete to construct a dome habitat on an asteroid to be mined.
See also
Cement-bonded wood fiber
Ground freezing, a construction technique using similar properties of frozen soil
Footnotes
References
External links
Pykrete - Ice Ships in the Rockies
Proposed WW2 aircraft carrier
Pykrete ... or, The Myth that Wouldn't Die...
Composite materials
Recycled building materials
Concrete
Water ice | Pykrete | [
"Physics",
"Engineering"
] | 2,043 | [
"Structural engineering",
"Composite materials",
"Materials",
"Concrete",
"Matter"
] |
340,952 | https://en.wikipedia.org/wiki/Genetic%20screen | A genetic screen or mutagenesis screen is an experimental technique used to identify and select individuals who possess a phenotype of interest in a mutagenized population. Hence a genetic screen is a type of phenotypic screen. Genetic screens can provide important information on gene function as well as the molecular events that underlie a biological process or pathway. While genome projects have identified an extensive inventory of genes in many different organisms, genetic screens can provide valuable insight as to how those genes function.
Basic screening
Forward genetics (or a forward genetic screen) starts with a phenotype and then attempts to identify the causative mutation and thus gene(s) responsible for the phenotype. For instance, the famous screen by Christiane Nüsslein-Volhard and Eric Wieschaus mutagenized fruit flies and then set out to find the genes causing the observed mutant phenotypes.
Successful forward genetic screens often require a defined genetic background and a simple experimental procedure. That is, when multiple individuals are mutagenized they should be genetically identical so that their wild-type phenotype is identical too and mutant phenotypes are easier to identify. A simple screening method allows for a larger number of individuals to be screened, thereby increasing the probability of generating and identifying mutants of interest.
Since natural allelic mutations are rare prior to screening geneticists often mutagenize a population of individuals by exposing them to a known mutagen, such as a chemical or radiation, thereby generating a much higher frequency of chromosomal mutations. In some organisms mutagens are used to perform saturation screens, that is, a screen used to uncover all genes involved in a particular phenotype. Christiane Nüsslein-Volhard and Eric Wieschaus were the first individuals to perform this type of screening procedure in animals.
Reverse genetics (or a reverse genetic screen), starts with a known gene and assays the effect of its disruption by analyzing the resultant phenotypes. For example, in a knock-out screen, one or more genes are completely deleted and the deletion mutants are tested for phenotypes. Such screens have been done for all genes in many bacteria and even complex organisms, such as C. elegans. A reverse genetic screen typically begins with a gene sequence followed by targeted inactivation. Moreover, it induces mutations in model organisms to learn their role in disease. Reverse genetics is also used to provide extremely accurate statistics on mutations that occur in specific genes. From these screens you are able to determine how fortuitous the mutations are, and how often the mutations occur.
Screening variations
Many screening variations have been devised to elucidate a gene that leads to a mutant phenotype of interest.
Enhancer
An enhancer screen begins with a mutant individual that has an affected process of interest with a known gene mutation. The screen can then be used to identify additional genes or gene mutations that play a role in that biological or physiological process. A genetic enhancer screen identifies mutations that enhance a phenotype of interest in an already mutant individual. The phenotype of the double mutant (individual with both the enhancer and original background mutation) is more prominent than either of the single mutant phenotypes. The enhancement must surpass the expected phenotypes of the two mutations on their own, and therefore each mutation may be considered an enhancer of the other. Isolating enhancer mutants can lead to the identification of interacting genes or genes which act redundantly with respect to one another.
Suppressor
A suppressor screen is used to identify suppressor mutations that alleviate or revert the phenotype of the original mutation, in a process defined as synthetic viability. Suppressor mutations can be described as second mutations at a site on the chromosome distinct from the mutation under study, which suppress the phenotype of the original mutation. If the mutation is in the same gene as the original mutation it is known as intragenic suppression, whereas a mutation located in a different gene is known as extragenic suppression or intergenic suppression. Suppressor mutations are extremely useful to define the functions of biochemical pathways within a cell and the relationships between different biochemical pathways.
Temperature sensitive
A temperature-sensitive screen involves performing temperature shifts to enhance a mutant phenotype. A population grown at low temperatures would have a normal phenotype; however, the mutation in the particular gene would make it unstable at a higher temperature. A screen for temperature sensitivity in fruit flies, for example, might involve raising the temperature in the cage until some flies faint, then opening a portal to let the others escape. Individuals selected in a screen are liable to carry an unusual version of a gene involved in the phenotype of interest. An advantage of alleles found in this type of screen is that the mutant phenotype is conditional and can be activated by simply raising the temperature. A null mutation in such a gene may be lethal to the embryo and such mutants would be missed in a basic screen. A famous temperature-sensitive screen was carried out independently by Lee Hartwell and Paul Nurse to identify mutants defective in the cell cycle in S. cerevisiae and S. pombe, respectively.
RNAi
RNA interference (RNAi) screen is essentially a forward genetics screen using a reverse genetics technique. Similar to classical genetic screens in the past, large-scale RNAi surveys success depends on a careful development of phenotypic assays and their interpretation. In Drosophila, RNAi has been applied in cultured cells or in vivo to investigate gene functions and to effect the function of single genes on a genome-wide scale. RNAi is used to silence gene expression in Drosophila by injecting dsRNA into early embryos, and interfering with Frizzled and Frizzled2 genes creating defects in embryonic patterning that mimic loss of wingless function.
CRISPR
CRISPR/Cas is primarily used for reverse genetic screens. CRISPR has the ability to create libraries of thousands of precise genetic mutations and can identify new tumors as well as validate older tumors in cancer research. Genome-scale CRISPR-Cas9 knockout (GeCKO) library targeting 18,080 genes with 64,751 unique guide sequences identify genes essential for cell viability in cancer. Bacterial CRISPR–Cas9 system for engineering both loss of function (LOF) and gain of function (GOF) mutations in untransformed human intestinal organoids in order to demonstrate a model of Colorectal cancer (CRC). It can also be used to study functional consequences of mutations in vivo by enabling direct genome editing in somatic cells.
Mapping mutants
By the classical genetics approach, a researcher would then locate (map) the gene on its chromosome by crossbreeding with individuals that carry other unusual traits and collecting statistics on how frequently the two traits are inherited together. Classical geneticists would have used phenotypic traits to map the new mutant alleles. With the advent of genomic sequences for model systems such as Drosophila melanogaster, Arabidopsis thaliana and C. elegans many single nucleotide polymorphisms (SNPs) have now been identified that can be used as traits for mapping. In fact, the Heidelberg screen, allowing mass testing of mutants and developed in 1980 by Nüsslein-Volhard and Wieschaus, cleared the way for future scientists in this field. SNPs are the preferred traits for mapping since they are very frequent, on the order of one difference per 1000 base pairs, between different varieties of organism. Mutagens such as random DNA insertions by transformation or active transposons can also be used to generate new mutants. These techniques have the advantage of tagging the new alleles with a known molecular (DNA) marker that can facilitate the rapid identification of the gene.
Positional cloning
Positional cloning is a method of gene identification in which a gene for a specific phenotype is identified only by its approximate chromosomal location (but not the function); this is known as the candidate region. Initially, the candidate region can be defined using techniques such as linkage analysis, and positional cloning is then used to narrow the candidate region until the gene and its mutations are found. Positional cloning typically involves the isolation of partially overlapping DNA segments from genomic libraries to progress along the chromosome toward a specific gene. During the course of positional cloning, one needs to determine whether the DNA segment currently under consideration is part of the gene.
Tests used for this purpose include cross-species hybridization, identification of unmethylated CpG islands, exon trapping, direct cDNA selection, computer analysis of DNA sequence, mutation screening in affected individuals, and tests of gene expression. For genomes in which the regions of genetic polymorphisms are known, positional cloning involves identifying polymorphisms that flank the mutation. This process requires that DNA fragments from the closest known genetic marker are progressively cloned and sequenced, getting closer to the mutant allele with each new clone. This process produces a contig map of the locus and is known as chromosome walking. With the completion of genome sequencing projects such as the Human Genome Project, modern positional cloning can use ready-made contigs from the genome sequence databases directly.
For each new DNA clone a polymorphism is identified and tested in the mapping population for its recombination frequency compared to the mutant phenotype. When the DNA clone is at or close to the mutant allele, the recombination frequency should be close to zero. If the chromosome walk proceeds through the mutant allele, the new polymorphisms will start to show increase in recombination frequency compared to the mutant phenotype. Depending on the size of the mapping population, the mutant allele can be narrowed down to a small region (<30 Kb). Sequence comparison between wild type and mutant DNA in that region is then required to locate the DNA mutation that causes the phenotypic difference.
Modern positional cloning can more directly extract information from genomic sequencing projects and existing data by analyzing the genes in the candidate region. Potential disease genes from the candidate region can then be prioritized, potentially reducing the amount of work involved. Genes with expression patterns consistent with the disease phenotype, showing a (putative) function related to the phenotype, or homologous to another gene linked to the phenotype are all priority candidates. Generalization of positional cloning techniques in this manner is also known as positional gene discovery.
Positional cloning is an effective method to isolate disease genes in an unbiased manner and has been used to identify disease genes for Duchenne muscular dystrophy, Huntington's disease, and cystic fibrosis. However, complications in the analysis arise if the disease exhibits locus heterogeneity.
References
External links
Principles of Map-based or Positional Cloning of Plant Genes
Nature Reviews Genetics Focus: The Art and Design of Genetic Screens
Classical genetics
Molecular genetics
Medical genetics
Genetics experiments | Genetic screen | [
"Chemistry",
"Biology"
] | 2,271 | [
"Molecular genetics",
"Molecular biology"
] |
340,982 | https://en.wikipedia.org/wiki/Petrology | Petrology () is the branch of geology that studies rocks, their mineralogy, composition, texture, structure and the conditions under which they form. Petrology has three subdivisions: igneous, metamorphic, and sedimentary petrology. Igneous and metamorphic petrology are commonly taught together because both make heavy use of chemistry, chemical methods, and phase diagrams. Sedimentary petrology is commonly taught together with stratigraphy because it deals with the processes that form sedimentary rock. Modern sedimentary petrology is making increasing use of chemistry.
Background
Lithology was once approximately synonymous with petrography, but in current usage, lithology focuses on macroscopic hand-sample or outcrop-scale description of rocks while petrography is the speciality that deals with microscopic details.
In the petroleum industry, lithology, or more specifically mud logging, is the graphic representation of geological formations being drilled through and drawn on a log called a mud log. As the cuttings are circulated out of the borehole, they are sampled, examined (typically under a 10× microscope) and tested chemically when needed.
Methodology
Petrology utilizes the fields of mineralogy, petrography, optical mineralogy, and chemical analysis to describe the composition and texture of rocks. Petrologists also include the principles of geochemistry and geophysics through the study of geochemical trends and cycles and the use of thermodynamic data and experiments in order to better understand the origins of rocks.
Branches
There are three branches of petrology, corresponding to the three types of rocks: igneous, metamorphic, and sedimentary, and another dealing with experimental techniques:
Igneous petrology focuses on the composition and texture of igneous rocks (rocks such as granite or basalt which have crystallized from molten rock or magma). Igneous rocks include volcanic and plutonic rocks.
Sedimentary petrology focuses on the composition and texture of sedimentary rocks (rocks such as sandstone, shale, or limestone which consist of pieces or particles derived from other rocks or biological or chemical deposits, and are usually bound together in a matrix of finer material).
Metamorphic petrology focuses on the composition and texture of metamorphic rocks (rocks such as slate, marble, gneiss, or schist) which have undergone chemical, mineralogical or textural changes due to the effects of pressure, temperature, or both). The original rock, prior to change (called the protolith), may be of any sort.
Experimental petrology employs high-pressure, high-temperature apparatus to investigate the geochemistry and phase relations of natural or synthetic materials at elevated pressures and temperatures. Experiments are particularly useful for investigating rocks of the lower crust and upper mantle that rarely survive the journey to the surface in pristine condition. They are also one of the prime sources of information about completely inaccessible rocks, such as those in the Earth's lower mantle and in the mantles of the other terrestrial planets and the Moon. The work of experimental petrologists has laid a foundation on which modern understanding of igneous and metamorphic processes has been built.
See also
Ore
Pedology
References
Citations
Sources
Best, Myron G. (2002), Igneous and Metamorphic Petrology (Blackwell Publishing) .
Blatt, Harvey; Tracy, Robert J.; Owens, Brent (2005), Petrology: igneous, sedimentary, and metamorphic (W. H. Freeman) .
Dietrich, Richard Vincent; Skinner, Brian J. (2009), Gems, Granites, and Gravels: knowing and using rocks and minerals (Cambridge University Press)
Fei, Yingwei; Bertka, Constance M.; Mysen, Bjorn O. (eds.) (1999), Mantle Petrology: field observations and high-pressure experimentation (Houston TX: Geochemical Society) .
Philpotts, Anthony; Ague, Jay (2009), Principles of Igneous and Metamorphic Petrology (Cambridge University Press)
Robb, L. (2005). Introduction to Ore-Forming Processes (Blackwell Science)
External links
Atlas of Igneous and metamorphic rocks, minerals, and textures – Geology Department, University of North Carolina
Metamorphic Petrology Database (MetPetDB) – Department of Earth and Environmental Sciences, Rensselaer Polytechnic Institute
Petrological Database of the Ocean Floor (PetDB) - Center for International Earth Science Information Network, Columbia University
Petroleum geology
Oilfield terminology | Petrology | [
"Chemistry"
] | 894 | [
"Petroleum",
"Petroleum geology"
] |
341,015 | https://en.wikipedia.org/wiki/Sparse%20matrix | In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., m × n for an m × n matrix) is sometimes referred to as the sparsity of the matrix.
Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system, as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The concept of sparsity is useful in combinatorics and application areas such as network theory and numerical analysis, which typically have a low density of significant data or connections. Large sparse matrices often appear in scientific or engineering applications when solving partial differential equations.
When storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. Specialized computers have been made for sparse matrices, as they are common in the machine learning field. Operations using standard dense-matrix structures and algorithms are slow and inefficient when applied to large sparse matrices as processing and memory are wasted on the zeros. Sparse data is by nature more easily compressed and thus requires significantly less storage. Some very large sparse matrices are infeasible to manipulate using standard dense-matrix algorithms.
Special cases
Banded
An important special type of sparse matrices is band matrix, defined as follows. The lower bandwidth of a matrix is the smallest number such that the entry vanishes whenever . Similarly, the upper bandwidth is the smallest number such that whenever . For example, a tridiagonal matrix has lower bandwidth and upper bandwidth . As another example, the following sparse matrix has lower and upper bandwidth both equal to 3. Notice that zeros are represented with dots for clarity.
Matrices with reasonably small upper and lower bandwidth are known as band matrices and often lend themselves to simpler algorithms than general sparse matrices; or one can sometimes apply dense matrix algorithms and gain efficiency simply by looping over a reduced number of indices.
By rearranging the rows and columns of a matrix it may be possible to obtain a matrix with a lower bandwidth. A number of algorithms are designed for bandwidth minimization.
Diagonal
A very efficient structure for an extreme case of band matrices, the diagonal matrix, is to store just the entries in the main diagonal as a one-dimensional array, so a diagonal matrix requires only entries.
Symmetric
A symmetric sparse matrix arises as the adjacency matrix of an undirected graph; it can be stored efficiently as an adjacency list.
Block diagonal
A block-diagonal matrix consists of sub-matrices along its diagonal blocks. A block-diagonal matrix has the form
where is a square matrix for all .
Use
Reducing fill-in
The fill-in of a matrix are those entries that change from an initial zero to a non-zero value during the execution of an algorithm. To reduce the memory requirements and the number of arithmetic operations used during an algorithm, it is useful to minimize the fill-in by switching rows and columns in the matrix. The symbolic Cholesky decomposition can be used to calculate the worst possible fill-in before doing the actual Cholesky decomposition.
There are other methods than the Cholesky decomposition in use. Orthogonalization methods (such as QR factorization) are common, for example, when solving problems by least squares methods. While the theoretical fill-in is still the same, in practical terms the "false non-zeros" can be different for different methods. And symbolic versions of those algorithms can be used in the same manner as the symbolic Cholesky to compute worst case fill-in.
Solving sparse matrix equations
Both iterative and direct methods exist for sparse matrix solving.
Iterative methods, such as conjugate gradient method and GMRES utilize fast computations of matrix-vector products , where matrix is sparse. The use of preconditioners can significantly accelerate convergence of such iterative methods.
Storage
A matrix is typically stored as a two-dimensional array. Each entry in the array represents an element of the matrix and is accessed by the two indices and . Conventionally, is the row index, numbered from top to bottom, and is the column index, numbered from left to right. For an matrix, the amount of memory required to store the matrix in this format is proportional to (disregarding the fact that the dimensions of the matrix also need to be stored).
In the case of a sparse matrix, substantial memory requirement reductions can be realized by storing only the non-zero entries. Depending on the number and distribution of the non-zero entries, different data structures can be used and yield huge savings in memory when compared to the basic approach. The trade-off is that accessing the individual elements becomes more complex and additional structures are needed to be able to recover the original matrix unambiguously.
Formats can be divided into two groups:
Those that support efficient modification, such as DOK (Dictionary of keys), LIL (List of lists), or COO (Coordinate list). These are typically used to construct the matrices.
Those that support efficient access and matrix operations, such as CSR (Compressed Sparse Row) or CSC (Compressed Sparse Column).
Dictionary of keys (DOK)
DOK consists of a dictionary that maps -pairs to the value of the elements. Elements that are missing from the dictionary are taken to be zero. The format is good for incrementally constructing a sparse matrix in random order, but poor for iterating over non-zero values in lexicographical order. One typically constructs a matrix in this format and then converts to another more efficient format for processing.
List of lists (LIL)
LIL stores one list per row, with each entry containing the column index and the value. Typically, these entries are kept sorted by column index for faster lookup. This is another format good for incremental matrix construction.
Coordinate list (COO)
COO stores a list of tuples. Ideally, the entries are sorted first by row index and then by column index, to improve random access times. This is another format that is good for incremental matrix construction.
Compressed sparse row (CSR, CRS or Yale format)
The compressed sparse row (CSR) or compressed row storage (CRS) or Yale format represents a matrix by three (one-dimensional) arrays, that respectively contain nonzero values, the extents of rows, and column indices. It is similar to COO, but compresses the row indices, hence the name. This format allows fast row access and matrix-vector multiplications (). The CSR format has been in use since at least the mid-1960s, with the first complete description appearing in 1967.
The CSR format stores a sparse matrix in row form using three (one-dimensional) arrays . Let denote the number of nonzero entries in . (Note that zero-based indices shall be used here.)
The arrays and are of length , and contain the non-zero values and the column indices of those values respectively
contains the column in which the corresponding entry is located.
The array is of length and encodes the index in and where the given row starts. This is equivalent to encoding the total number of nonzeros above row . The last element is , i.e., the fictitious index in immediately after the last valid index .
For example, the matrix
is a matrix with 4 nonzero elements, hence
V = [ 5 8 3 6 ]
COL_INDEX = [ 0 1 2 1 ]
ROW_INDEX = [ 0 1 2 3 4 ]
assuming a zero-indexed language.
To extract a row, we first define:
row_start = ROW_INDEX[row]
row_end = ROW_INDEX[row + 1]
Then we take slices from V and COL_INDEX starting at row_start and ending at row_end.
To extract the row 1 (the second row) of this matrix we set row_start=1 and row_end=2. Then we make the slices V[1:2] = [8] and COL_INDEX[1:2] = [1]. We now know that in row 1 we have one element at column 1 with value 8.
In this case the CSR representation contains 13 entries, compared to 16 in the original matrix. The CSR format saves on memory only when .
Another example, the matrix
is a matrix (24 entries) with 8 nonzero elements, so
V = [ 10 20 30 40 50 60 70 80 ]
COL_INDEX = [ 0 1 1 3 2 3 4 5 ]
ROW_INDEX = [ 0 2 4 7 8 ]
The whole is stored as 21 entries: 8 in , 8 in , and 5 in .
splits the array into rows: (10, 20) (30, 40) (50, 60, 70) (80), indicating the index of (and ) where each row starts and ends;
aligns values in columns: (10, 20, ...) (0, 30, 0, 40, ...)(0, 0, 50, 60, 70, 0) (0, 0, 0, 0, 0, 80).
Note that in this format, the first value of is always zero and the last is always , so they are in some sense redundant (although in programming languages where the array length needs to be explicitly stored, would not be redundant). Nonetheless, this does avoid the need to handle an exceptional case when computing the length of each row, as it guarantees the formula works for any row . Moreover, the memory cost of this redundant storage is likely insignificant for a sufficiently large matrix.
The (old and new) Yale sparse matrix formats are instances of the CSR scheme. The old Yale format works exactly as described above, with three arrays; the new format combines and into a single array and handles the diagonal of the matrix separately.
For logical adjacency matrices, the data array can be omitted, as the existence of an entry in the row array is sufficient to model a binary adjacency relation.
It is likely known as the Yale format because it was proposed in the 1977 Yale Sparse Matrix Package report from Department of Computer Science at Yale University.
Compressed sparse column (CSC or CCS)
CSC is similar to CSR except that values are read first by column, a row index is stored for each value, and column pointers are stored. For example, CSC is , where is an array of the (top-to-bottom, then left-to-right) non-zero values of the matrix; is the row indices corresponding to the values; and, is the list of indexes where each column starts. The name is based on the fact that column index information is compressed relative to the COO format. One typically uses another format (LIL, DOK, COO) for construction. This format is efficient for arithmetic operations, column slicing, and matrix-vector products. This is the traditional format for specifying a sparse matrix in MATLAB (via the sparse function).
Software
Many software libraries support sparse matrices, and provide solvers for sparse matrix equations. The following are open-source:
PETSc, a large C library, containing many different matrix solvers for a variety of matrix storage formats.
Trilinos, a large C++ library, with sub-libraries dedicated to the storage of dense and sparse matrices and solution of corresponding linear systems.
Eigen3 is a C++ library that contains several sparse matrix solvers. However, none of them are parallelized.
MUMPS (MUltifrontal Massively Parallel sparse direct Solver), written in Fortran90, is a frontal solver.
deal.II, a finite element library that also has a sub-library for sparse linear systems and their solution.
DUNE, another finite element library that also has a sub-library for sparse linear systems and their solution.
Armadillo provides a user-friendly C++ wrapper for BLAS and LAPACK.
SciPy provides support for several sparse matrix formats, linear algebra, and solvers.
ALGLIB is a C++ and C# library with sparse linear algebra support
ARPACK Fortran 77 library for sparse matrix diagonalization and manipulation, using the Arnoldi algorithm
SLEPc Library for solution of large scale linear systems and sparse matrices
scikit-learn, a Python library for machine learning, provides support for sparse matrices and solvers
SparseArrays is a Julia standard library.
PSBLAS, software toolkit to solve sparse linear systems supporting multiple formats also on GPU.
History
The term sparse matrix was possibly coined by Harry Markowitz who initiated some pioneering work but then left the field.
See also
Notes
References
(This book, by a professor at the State University of New York at Stony Book, was the first book exclusively dedicated to Sparse Matrices. Graduate courses using this as a textbook were offered at that University in the early 1980s).
Also NOAA Technical Memorandum NOS NGS-4, National Geodetic Survey, Rockville, MD. Referencing .
(Open Access)
Further reading
Sparse Matrix Algorithms Research at the Texas A&M University.
SuiteSparse Matrix Collection
SMALL project A EU-funded project on sparse models, algorithms and dictionary learning for large-scale data.
Arrays | Sparse matrix | [
"Mathematics"
] | 2,836 | [
"Matrices (mathematics)",
"Sparse matrices",
"Mathematical objects",
"Combinatorics"
] |
341,029 | https://en.wikipedia.org/wiki/Urban%20geography | Urban geography is the subdiscipline of geography that derives from a study of cities and urban processes. Urban geographers and urbanists examine various aspects of urban life and the built environment. Scholars, activists, and the public have participated in, studied, and critiqued flows of economic and natural resources, human and non-human bodies, patterns of development and infrastructure, political and institutional activities, governance, decay and renewal, and notions of socio-spatial inclusions, exclusions, and everyday life. Urban geography includes different other fields in geography such as the physical, social, and economic aspects of urban geography. The physical geography of urban environments is essential to understand why a town is placed in a specific area, and how the conditions in the environment play an important role with regards to whether or not the city successfully develops. Social geography examines societal and cultural values, diversity, and other conditions that relate to people in the cities. Economic geography is important to examine the economic and job flow within the urban population. These various aspects involved in studying urban geography are necessary to better understand the layout and planning involved in the development of urban environments worldwide.
Patterns of Urban Development and Infrastructure
The development pattern of a place such as city, neighborhood deals how the building and human activities are arranged and organized on the landscape. Urban environments are composed of hard infrastructure, such as roads and bridges, and soft infrastructure, such as health and social services. The construction of urban areas is facilitated through urban planning and architecture. To combat the negative environmental effects of urban development, green infrastructure such as community gardens and parks, sewage and waste systems, and the use of solar energy have been implemented in many cities. The use of green infrastructure has been effective in responding to climate change and reducing flood risks. Green infrastructure, such as home and urban gardens, have been found to not only improve air quality but also promote mental well-being.
Flow of Economic and Natural Resources Within Urban Environments
Over the years, the development of urban environments has continued to increase due to globalization and urbanization. According to the UN, the world's population in urban areas is estimated to increase from 55% to 68% by the year 2050. The increase in the development of urban environments leads to the increase in economic flow and utilization of natural resources. As the population in urban areas continue to grow, the use of direct energy and transport energy tends to increase and is estimated to increase in the future.
According to the study conducted by Creutzig et al., the current energy usage is projected to increase from 240 EJ in 2005 to 730 EJ in the year 2050 if worldwide urbanization continues. As more people move to the cities in search of work, business tends to follow suit. Thus, cities will develop the need for new infrastructures such as schools, hospitals, and various public facilities. The development of these types of soft infrastructure can lead to a positive impact on the residents. For instance, soft infrastructure can promote economic growth through allowing its residents to specialize in different areas of expertise. The diversification of careers within the urban population can increase the economic flow within the urban area.
Human Interactions Within Urban Environments
The development of soft infrastructure within urban areas provide people with ways to connect with one another as a community as well as ways to seek support services. Community infrastructure includes areas and services that allow human beings to interact with one another. Such interactions can be facilitated through health services, educational institutions, outreach centers, and community groups. Human interactions with their urban environments can lead to both positive and negative effects. Humans depend on their environment in order to get essential resources, such as good air quality, food and shelter. This natural environmental dependence can lead to the over exploitation of natural resources as the need for such resources increase. Humans can also modify their environment in order to meet their goals. For instance, humans can clear land or agriculture in order to develop urbanized buildings such as commercial skyscrapers and public housing. The clearing of land to pave the way for urbanization can lead to negative environmental impacts such as deforestation, decreased air quality, and wild life displacement.
Social and Political Flow Within Urban Environments
As populations within cities grew over the years, the need to create forms of local government emerged. To maintain order within developing cities, politicians are elected to address environmental and societal issues within the population. For instance, the influence of local and state political dynamics plays an important role in how actions are taken place to combat climate change and housing issues.
Impact of Urban Geography
Environmental Impact
The environment of urban areas is developed through the concept of urbanization. Urbanization is the transition from rural town-structured communities to urban city-structured communities. This transition is because humans are pulled to cities because of jobs and even welfare. In cities, problems will arise such as environmental degradation. The increasing population can lead to poor air quality and quality and availability of water. The growth of urbanization can lead to more use of energy which leads to air pollution and can impact human health. Flash flooding is another environmental hazard that can occur due to urban development. The concept of urbanization plays an important role in the study of urban geography because it involves the formation of urban infrastructures such as sanitation, sewage systems, and the distribution of electricity and gas.
Societal Impact
The migration form rural to urbanized areas is fueled by their search for jobs, education, and social welfare. There are trends in urbanization that are influenced by push and pull factors. The push factors include the increasingly high growth of rural areas which leads many people to migrate to the cities in search of better livelihood opportunities, a good quality of life, and a higher standard of living. People are forced to leave their rural homes and move to various cities because of various factors such as low agricultural productivity, poverty, and food insecurity. In addition to the push factors, there are also the pull factors, which "pull" people to cities for better opportunities, better education, proper public health facilities, and also entertainment which offers employment opportunities. The gentrification of urban environments leads to an increase in income gaps, racial inequality, and displacement within metropolitan areas. The negative environmental impacts of urbanization disproportionately effects minority low income areas more than higher income communities.
Climate Impact
The increasing demand for new building infrastructure within densely populated cities resulted in an increase in air pollution due to the high energy usage within these urban areas. The increasing energy use leads to an increase in heat emissions, which results in global warming. Cities are a key contributor to climate change because urban activities are a major source of greenhouse gas emissions. It was estimated that cities are responsible for about 75% of global carbon dioxide emissions, with the inclusion of transportation and buildings being the largest contributor. In order to combat the negative environmental impacts urbanization, many modern cities develop environmentally conscious infrastructure. For instance, the implementation of public transportation such as train and bus systems help to lessen the use of cars within cities. The use of solar energy can also be found in many commercial and residential buildings, which helps to lessen the reliance on non-renewable energy resources.
Biodiversity Impact
Urbanization has a great impact on biodiversity. As cities develop, vital habitats are destroyed or fragmented into patches which leads to them not being big enough to support complex ecological communities. In cities, species can become endangered or locally extinct. The human population is the main contributor to the expansion of urban areas. As urban areas grow from increasing human population and from migration, this can result in deforestation, habitat loss, and extraction of freshwater from the environment which can decrease biodiversity and alter the species ranges and interaction. Some additional cause-and-effect relationships between urban geography and ecosystems include habitat loss which decreases the species' populations, ranges, and interaction among organisms, the life cycles, and traits can help species survive and reproduce in disturbed ecosystems. The paving of land with concrete can increase water runoff, increase erosion, and soil quality can also decrease.
Research interest
Urban geographers are primarily concerned with the ways in which cities and towns are constructed, governed and experienced. Alongside neighboring disciplines such as urban anthropology, urban planning and urban sociology, urban geography mostly investigates the impact of urban processes on the earth's surface's social and physical structures. Urban geographical research can be part of both human geography and physical geography.
The two fundamental aspects of cities and towns, from the geographic perspective are:
Location ("systems of cities"): spatial distribution and the complex patterns of movement, flows and linkages that bind them in space; and
Urban structure ("cities as systems"): study of patterns of distribution and interaction within cities, from quantitative, qualitative, structural, and behavioral perspectives.
Research topics
Cities as centers of manufacturing and services
Cities differ in their economic makeup, their social and demographic characteristics, and the roles they play within the city system. One can trace these differences back to regional variations in the local resources on which growth was based during the early development of the urban pattern and in part to the subsequent shifts in the competitive advantage of regions brought about by changing locational forces affecting regional specialization within the framework of a market economy. The recognition of different city types is critical for the classification of cities in urban geography. For such classification, emphasis given in particular to functional town classification and the basic underlying dimensions of the city system.
The purpose of classifying cities is twofold. On the one hand, it is undertaken to search reality for hypotheses. In this context, the recognition of different types of cities on the basis of, for example, their functional specialization may enable the identification of spatial regularities in the distribution and structure of urban functions and the formulation of hypotheses about the resulting patterns. On the other hand, classification is undertaken to structure reality in order to test specific hypotheses that have already been formulated. For example, to test the hypotheses that cities with a diversified economy grow at a faster rate then those with a more specialized economic base, cities must first be classified so that diversified and specialized cities can be differentiated.
The simplest way to classify cities is to identify the distinctive role they play in the city system. There are three distinct roles:
central places functioning primarily as service centers for local hinterlands
transportation cities performing break-of-bulk and allied functions for larger regions
specialized-function cities, dominated by one activity such as mining, manufacturing or recreation and serving national and international markets
The composition of a city's labor force has traditionally been regarded as the best indicator of functional specialization, and different city types have been most frequently identified from the analysis of employment profiles. Specialization in a given activity is said to exist when employment in it exceeds some critical level.
The relationship between the city system and the development of manufacturing has become very apparent. The rapid growth and spread of cities within the heartland-hinterland framework after 1870 was conditioned to a large extent by industrial developments, and the decentralization of population within the urban system in recent years is related in large part to the movement of employment in manufacturing away from traditional industrial centers. Manufacturing is found in nearly all cities, but its importance is measured by the proportion of total earnings received by the inhabitants of an urban area. When 25 percent or more of the total earnings in an urban region derive from manufacturing, that urban area is arbitrarily designated as a manufacturing center.
The location of manufacturing is affected by myriad economic and non-economic factors, such as the nature of the material inputs, the factors of production, the market and transportation costs. Other important influences include agglomeration and external economies, public policy and personal preferences. Although it is difficult to evaluate precisely the effect of the market on the location of manufacturing activities, two considerations are involved:
the nature of and demand for the product
transportation costs
Urbanization
Urbanization, the transformation of population from rural to urban, is a major phenomenon of the modern era and a central topic of study.
History of the discipline
Urban geography arrived as a critical sub-discipline with the 1973 publication of David Harvey's Social Justice and the City, which was heavily influenced by previous work by Anne Buttimer. Prior to its emergence as its own discipline, urban geography served as the academic extension of what was otherwise a professional development and planning practice. At the turn of the 19th century, urban planning began as a profession charged with mitigating the negative consequences of industrialization as documented by Friedrich Engels in his geographic analysis of the condition of the working class in England, 1844.
In a 1924 study of urban geography, Marcel Aurousseau observed that urban geography cannot be considered a subdivision of geography because it plays such an important part. However, urban geography did emerge as a specialized discipline after World War II, amidst increasing urban planning and a shift away from the primacy of physical terrain in the study of geography. Chauncy Harris and Edward Ullman were among its earliest exponents.
Urban geography arose by the 1930s in the Soviet Union as an academic complement to active urbanization and communist urban planning, focusing on cities' economic roles and potential.
Spatial analysis, behavioral analysis, Marxism, humanism, social theory, feminism, and postmodernism have arisen (in approximately this order) as overlapping lenses used within the field of urban geography in the West.
Geographic information science, using digital processing of large data sets, has become widely used since the 1980s, with major applications for urban geography.
Notable urban geographers and urbanists
Ash Amin
Mike Batty
Walter Benjamin
Anne Buttimer
Michel de Certeau
Tim Cresswell
Mike Davis
Friedrich Engels
Matthew Gandy
Peter Hall (urbanist)
Milton Santos
David Harvey
Jane Jacobs
Henri Lefebvre
David Ley
Peter Marcuse
Doreen Massey
Don Mitchell
Aihwa Ong
Gillian Rose (geographer)
Ananya Roy
Neil Smith (geographer)
Allen J. Scott
Edward W. Soja
Michael Storper
Fulong Wu
Akin Mabogunje
Loretta Lees
See also
Arbia's law of geography
Chicago school (sociology)
Commuter town
Concepts and Techniques in Modern Geography
Garden city movement
Gentrification
Index of urban studies articles
Infrastructure
Municipal or urban engineering
Rural sociology
Settlement geography
Tobler's first law of geography
Tobler's second law of geography
Urban agriculture
Urban area
Urban ecology
Urban economics
Urban field
Urban sociology
Urban studies
Urban vitality
References
External links
Imagining Urban Futures
Social and Spatial Inequalities
Urban Geography Specialty Group of the Association of American Geographers
Urban Geography Research Group of the Royal Geographical Society-Institute of British Geographers
Urbanization
Urban planning | Urban geography | [
"Engineering"
] | 2,938 | [
"Urban planning",
"Architecture"
] |
341,038 | https://en.wikipedia.org/wiki/Reporter%20gene | In molecular biology, a reporter gene (often simply reporter) is a gene that researchers attach to a regulatory sequence of another gene of interest in bacteria, cell culture, animals or plants. Such genes are called reporters because the characteristics they confer on organisms expressing them are easily identified and measured, or because they are selectable markers. Reporter genes are often used as an indication of whether a certain gene has been taken up by or expressed in the cell or organism population.
Common reporter genes
To introduce a reporter gene into an organism, scientists place the reporter gene and the gene of interest in the same DNA construct to be inserted into the cell or organism. For bacteria or prokaryotic cells in culture, this is usually in the form of a circular DNA molecule called a plasmid. For viruses, this is known as a viral vector. It is important to use a reporter gene that is not natively expressed in the cell or organism under study, since the expression of the reporter is being used as a marker for successful uptake of the gene of interest.
Commonly used reporter genes that induce visually identifiable characteristics usually involve fluorescent and luminescent proteins. Examples include the gene that encodes jellyfish green fluorescent protein (GFP), which causes cells that express it to glow green under blue or ultraviolet light, the enzyme luciferase, which catalyzes a reaction with luciferin to produce light, and the red fluorescent protein from the gene . The GUS gene has been commonly used in plants but luciferase and GFP are becoming more common.
A common reporter in bacteria is the E. coli lacZ gene, which encodes the protein beta-galactosidase. This enzyme causes bacteria expressing the gene to appear blue when grown on a medium that contains the substrate analog X-gal. An example of a selectable marker which is also a reporter in bacteria is the chloramphenicol acetyltransferase (CAT) gene, which confers resistance to the antibiotic chloramphenicol.
Transformation and transfection assays
Many methods of transfection and transformation – two ways of expressing a foreign or modified gene in an organism – are effective in only a small percentage of a population subjected to the techniques. Thus, a method for identifying those few successful gene uptake events is necessary. Reporter genes used in this way are normally expressed under their own promoter (DNA regions that initiates gene transcription) independent from that of the introduced gene of interest; the reporter gene can be expressed constitutively (that is, it is "always on") or inducibly with an external intervention such as the introduction of Isopropyl β-D-1-thiogalactopyranoside (IPTG) in the β-galactosidase system. As a result, the reporter gene's expression is independent of the gene of interest's expression, which is an advantage when the gene of interest is only expressed under certain specific conditions or in tissues that are difficult to access.
In the case of selectable-marker reporters such as CAT, the transfected population of bacteria can be grown on a substrate that contains chloramphenicol. Only those cells that have successfully taken up the construct containing the CAT gene will survive and multiply under these conditions.
Gene expression assays
Reporter genes can be used to assay for the expression of a gene of interest that is normally difficult to quantitatively assay. Reporter genes can produce a protein that has little obvious or immediate effect on the cell culture or organism. They are ideally not present in the native genome to be able to isolate reporter gene expression as a result of the gene of interest's expression.
To activate reporter genes, they can be expressed constitutively, where they are directly attached to the gene of interest to create a gene fusion. This method is an example of using cis-acting elements where the two genes are under the same promoter elements and are transcribed into a single messenger RNA molecule. The mRNA is then translated into protein. It is important that both proteins be able to properly fold into their active conformations and interact with their substrates despite being fused. In building the DNA construct, a segment of DNA coding for a flexible polypeptide linker region is usually included so that the reporter and the gene product will only minimally interfere with one another. Reporter genes can also be expressed by induction during growth. In these cases, trans-acting elements, such as transcription factors are used to express the reporter gene.
Reporter gene assay have been increasingly used in high throughput screening (HTS) to identify small molecule inhibitors and activators of protein targets and pathways for drug discovery and chemical biology. Because the reporter enzymes themselves (e.g. firefly luciferase) can be direct targets of small molecules and confound the interpretation of HTS data, novel coincidence reporter designs incorporating artifact suppression have been developed.
Promoter assays
Reporter genes can be used to assay for the activity of a particular promoter in a cell or organism. In this case there is no separate "gene of interest"; the reporter gene is simply placed under the control of the target promoter and the reporter gene product's activity is quantitatively measured. The results are normally reported relative to the activity under a "consensus" promoter known to induce strong gene expression.
Further uses
A more complex use of reporter genes on a large scale is in two-hybrid screening, which aims to identify proteins that natively interact with one another in vivo.
See also
GUS reporter system
References
External links
Research highlights and updated information on reporter genes.
Staining Whole Mouse Embryos for β-Galactosidase (lacZ) Activity
Biochemistry detection methods
Genetics techniques
Molecular biology
es:Gen reportero | Reporter gene | [
"Chemistry",
"Engineering",
"Biology"
] | 1,172 | [
"Biochemistry methods",
"Genetics techniques",
"Genetic engineering",
"Chemical tests",
"Biochemistry detection methods",
"Molecular biology",
"Biochemistry"
] |
341,046 | https://en.wikipedia.org/wiki/Green%20algae | The green algae (: green alga) are a group of chlorophyll-containing autotrophic eukaryotes consisting of the phylum Prasinodermophyta and its unnamed sister group that contains the Chlorophyta and Charophyta/Streptophyta. The land plants (Embryophytes) have emerged deep within the charophytes as a sister of the Zygnematophyceae. Since the realization that the Embryophytes emerged within the green algae, some authors are starting to include them. The completed clade that includes both green algae and embryophytes is monophyletic and is referred to as the clade Viridiplantae and as the kingdom Plantae. The green algae include unicellular and colonial flagellates, most with two flagella per cell, as well as various colonial, coccoid (spherical), and filamentous forms, and macroscopic, multicellular seaweeds. There are about 22,000 species of green algae, many of which live most of their lives as single cells, while other species form coenobia (colonies), long filaments, or highly differentiated macroscopic seaweeds.
A few other organisms rely on green algae to conduct photosynthesis for them. The chloroplasts in dinoflagellates of the genus Lepidodinium, euglenids and chlorarachniophytes were acquired from ingested endosymbiont green algae, and in the latter retain a nucleomorph (vestigial nucleus). Green algae are also found symbiotically in the ciliate Paramecium, and in Hydra viridissima and in flatworms. Some species of green algae, particularly of genera Trebouxia of the class Trebouxiophyceae and Trentepohlia (class Ulvophyceae), can be found in symbiotic associations with fungi to form lichens. In general the fungal species that partner in lichens cannot live on their own, while the algal species is often found living in nature without the fungus. Trentepohlia is a filamentous green alga that can live independently on humid soil, rocks or tree bark or form the photosymbiont in lichens of the family Graphidaceae. Also the macroalga Prasiola calophylla (Trebouxiophyceae) is terrestrial, and
Prasiola crispa, which live in the supralittoral zone, is terrestrial and can in the Antarctic form large carpets on humid soil, especially near bird colonies.
Cellular structure
Green algae have chloroplasts that contain chlorophyll a and b, giving them a bright green colour, as well as the accessory pigments beta carotene (red-orange) and xanthophylls (yellow) in stacked thylakoids. The cell walls of green algae usually contain cellulose, and they store carbohydrate in the form of starch.
All green algae have mitochondria with flat cristae. When present, paired flagella are used to move the cell. They are anchored by a cross-shaped system of microtubules and fibrous strands. Flagella are only present in the motile male gametes of charophytes bryophytes, pteridophytes, cycads and Ginkgo, but are absent from the gametes of Pinophyta and flowering plants.
Members of the class Chlorophyceae undergo closed mitosis in the most common form of cell division among the green algae, which occurs via a phycoplast. By contrast, charophyte green algae and land plants (embryophytes) undergo open mitosis without centrioles. Instead, a 'raft' of microtubules, the phragmoplast, is formed from the mitotic spindle and cell division involves the use of this phragmoplast in the production of a cell plate.
Origins
Photosynthetic eukaryotes originated following a primary endosymbiotic event, where a heterotrophic eukaryotic cell engulfed a photosynthetic cyanobacterium-like prokaryote that became stably integrated and eventually evolved into a membrane-bound organelle: the plastid. This primary endosymbiosis event gave rise to three autotrophic clades with primary plastids: the (green) plants (with chloroplasts) the red algae (with rhodoplasts) and the glaucophytes (with muroplasts).
Evolution and classification
Green algae are often classified with their embryophyte descendants in the green plant clade Viridiplantae (or Chlorobionta). Viridiplantae, together with red algae and glaucophyte algae, form the supergroup Primoplantae, also known as Archaeplastida or Plantae sensu lato. The ancestral green alga was a unicellular flagellate.
The Viridiplantae diverged into two clades. The Chlorophyta include the early diverging prasinophyte lineages and the core Chlorophyta, which contain the majority of described species of green algae. The Streptophyta include charophytes and land plants. Below is a consensus reconstruction of green algal relationships, mainly based on molecular data.
The basal character of the Mesostigmatophyceae, Chlorokybophyceae and spirotaenia are only more conventionally basal Streptophytes.
The algae of this paraphyletic group "Charophyta" were previously included in Chlorophyta, so green algae and Chlorophyta in this definition were synonyms. As the green algae clades get further resolved, the embryophytes, which are a deep charophyte branch, are included in "algae", "green algae" and "Charophytes", or these terms are replaced by cladistic terminology such as Archaeplastida, Plantae/Viridiplantae, and streptophytes, respectively.
Reproduction
Green algae are a group of photosynthetic, eukaryotic organisms that include species with haplobiontic and diplobiontic life cycles. The diplobiontic species, such as Ulva, follow a reproductive cycle called alternation of generations in which two multicellular forms, haploid and diploid, alternate, and these may or may not be isomorphic (having the same morphology). In haplobiontic species only the haploid generation, the gametophyte is multicellular. The fertilized egg cell, the diploid zygote, undergoes meiosis, giving rise to haploid cells which will become new gametophytes. The diplobiontic forms, which evolved from haplobiontic ancestors, have both a multicellular haploid generation and a multicellular diploid generation. Here the zygote divides repeatedly by mitosis and grows into a multicellular diploid sporophyte. The sporophyte produces haploid spores by meiosis that germinate to produce a multicellular gametophyte. All land plants have a diplobiontic common ancestor, and diplobiontic forms have also evolved independently within Ulvophyceae more than once (as has also occurred in the red and brown algae).
Diplobiontic green algae include isomorphic and heteromorphic forms. In isomorphic algae, the morphology is identical in the haploid and diploid generations. In heteromorphic algae, the morphology and size are different in the gametophyte and sporophyte.
Reproduction varies from fusion of identical cells (isogamy) to fertilization of a large non-motile cell by a smaller motile one (oogamy). However, these traits show some variation, most notably among the basal green algae called prasinophytes.
Haploid algal cells (containing only one copy of their DNA) can fuse with other haploid cells to form diploid zygotes. When filamentous algae do this, they form bridges between cells, and leave empty cell walls behind that can be easily distinguished under the light microscope. This process is called conjugation and occurs for example in Spirogyra.
Sex pheromone
Sex pheromone production is likely a common feature of green algae, although only studied in detail in a few model organisms. Volvox is a genus of chlorophytes. Different species form spherical colonies of up to 50,000 cells. One well-studied species, Volvox carteri (2,000 – 6,000 cells) occupies temporary pools of water that tend to dry out in the heat of late summer. As their environment dries out, asexual V. carteri quickly die. However, they are able to escape death by switching, shortly before drying is complete, to the sexual phase of their life cycle that leads to production of dormant desiccation-resistant zygotes. Sexual development is initiated by a glycoprotein pheromone (Hallmann et al., 1998). This pheromone is one of the most potent known biological effector molecules. It can trigger sexual development at concentrations as low as 10−16M. Kirk and Kirk showed that sex-inducing pheromone production can be triggered experimentally in somatic cells by heat shock. Thus heat shock may be a condition that ordinarily triggers sex-inducing pheromone in nature.
The Closterium peracerosum-strigosum-littorale (C. psl) complex is a unicellular, isogamous charophycean alga group that is the closest unicellular relative to land plants. Heterothallic strains of different mating type can conjugate to form zygospores. Sex pheromones termed protoplast-release inducing proteins (glycopolypeptides) produced by mating-type (-) and mating-type (+) cells facilitate this process.
Physiology
The green algae, including the characean algae, have served as model experimental organisms to understand the mechanisms of the ionic and water permeability of membranes, osmoregulation, turgor regulation, salt tolerance, cytoplasmic streaming, and the generation of action potentials.
References
External links
Green algae and cyanobacteria in lichens
Green algae (UC Berkeley)
Monterey Bay green algae
Green algae
Paraphyletic groups | Green algae | [
"Biology"
] | 2,260 | [
"Phylogenetics",
"Algae",
"Paraphyletic groups",
"Green algae"
] |
341,059 | https://en.wikipedia.org/wiki/Amami%20rabbit | The Amami rabbit (Pentalagus furnessi), also known as the Ryukyu rabbit is a dark-furred species of rabbit which is found only on Amami Ōshima and Tokunoshima, two small islands between southern Kyūshū and Okinawa in Japan. Often called a living fossil, the Amami rabbit is a living remnant of ancient rabbits that once lived on the Asian mainland, where they died out, remaining only on the two small Japanese islands where they live today.
Evolution
Pentalagus is thought to be a descendant of Pliopentalagus, known from the Pliocene of China and Eastern to Central Europe. It is also closely related to the North American genus Aztlanolagus (which may be synonynous with Pliopentalagus), which became extinct sometime after 30,000 years ago. The closest living relative of the Amani rabbit has been suggested to be the Central African Bunyoro rabbit (Poelagus marjorita).
Etymology
The generic name Pentalagus, as described by Marcus Ward Lyon Jr., refers to the presence of five molars on each side of the Amami rabbit's teeth, differing from each other extant then-known rabbit genera in that it lacks a third upper molar. The specific name furnessi refers to the original discoverer of the Amami rabbit, William Henry Furness III.
Biology
Diet
The Amami rabbit feeds on over 29 species of plants, which incorporates 17 species of shrubs and 12 species of herbaceous plants, consuming mostly the sprouts, young shoots and acorns. It also eats nuts and cambium of a wide variety of plant species. It is observed that the Amami rabbit also feeds on the bark of stems and twigs of shrub plants. During summer, the Amami rabbit primarily feeds on Japanese pampas grass, and during winter, they primarily eat the acorns of the pasania tree. The Amami rabbit also eats the fruits of Balanophora yuwanensis, a parasitic flowering plant, for which they are the main distributors of seed.
Morphology
The Amami rabbit has short feet and hind legs, a somewhat bulky body, and rather large and curved claws used for digging and sometimes climbing. Its ears are significantly smaller compared to those of other hares or rabbits. The pelage is thick, wooly and dark, brown on top and becomes more reddish-brown on the sides. It has heavy, long and very strong claws, being nearly straight on the forefeet and curved on the hindfeet The eyes are also small compared to more common rabbits and hares. The average weight is 2.5–2.8 kg.
Distribution and habitat
The ideal habitat for these rabbits is in an area between mature and young forests. They use the dense mature forests as protection and for the presence of pampas grass, in the summer, and acorns, in the winter, for their diets. They also use the high density of perennial grasses and herbaceous ground cover in the young forests for their diets during different times of the year. Therefore, the best habitat for them to live in is where they have easy access to both young and mature forests with no obstructions between the two forest types.
Using fecal pellet counts and resident surveys, the number of rabbits is estimated at 2000–4800 left on Amami Island and 120–300 left on Tokuno Island.
Behavior
This species is a nocturnal forest-dweller that reproduces once in late March–May and once in September–December, having one or two young each time. During the day, the mother digs a hole in the ground, for her young to hide in. At night, she opens the entrance to the hole, while watching for predators (such as venomous snakes), and then nurses her young, after which she closes the hole with soil and plant material by thumping on it with her front paws. Amami rabbits sleep during the day in hidden locations, such as caves. They are also noted for having a call similar to that of a pika.
Endangered species
Threats
Before 1921, hunting and trapping were another cause of decline in population numbers. In 1921, Japan declared the Amami rabbit a "natural monument" which prevented it from being hunted. Then in 1963, it was changed to a "special natural monument" which prevented it from being trapped as well.
Habitat destruction, such as forest clearing for commercial logging, agriculture space, and residential areas, is the most detrimental activity on the distribution of these rabbits. Since they prefer a habitat of both mature and young forests, they do not thrive in only mature forests untouched by destruction, yet they do not thrive in newly growing forests alone, either. There are plans to remove the current habitat for these rabbits for the construction of golf courses and resorts, which is allowed because it will not directly be killing the rabbit, just changing the environment where it dwells, which is legal even under the protection of the special natural monument status.
The Amami rabbit also faces huge threats from the invasive predators, being a major cause for the decline in population size. On the island of Amami, the small Indian mongoose (Urva auropunctata) was released to control the population of a local venomous snake, and its numbers have increased dramatically. This mongoose, along with feral cats and dogs, are outpreying the Amami rabbit. Feral cats and small Indian Mongooses proved to be a threat to not only Amami rabbits but several other endangered endemic species in the area such as the Amami jay.
Conservation
In July 2008, the Amami Rangers for nature conservation obtained a photograph of a feral cat carrying a rabbit corpse (rabbit bones and fur found in cat or dog droppings had already been found), prompting discussions on better ways to control pets. A small area of the Amami Island has the Amami Guntō National Park that further protects the population. Some attempt at habitat restoration has been made, but the Amami rabbit needs a mosaic of mature and young forest in close proximity, and when a young forest is regrown nowhere near a mature forest, this rabbit is not likely to inhabit it. Research and population monitoring also is underway to try to keep the numbers from declining, even if they can not be increased.
Suggested conservation work for the future includes habitat restoration and predator population control, as a healthy balance of mature and young forests still exists on the southern end of Amami. Restricting logging would also help to keep more forest available for the rabbits to live in by leaving more forest standing, as well as disturbing the surrounding environment more. An end to the building of forest roads used for logging and travel would further protect the Amami rabbit, as they cause population and habitat fragmentation, destroys their prime habitat and allows predators easier access to the middle of forests where a majority of the rabbit population exists. Controlling the populations of mongooses, feral dogs, and feral cats is another approach that could help bolster the rabbit population. Eradication of the mongooses and feral cats and dogs is needed, as well as better control of pets by local island residents.
The Lagomorph Specialist Group of the International Union for the Conservation of Nature and Natural Resources proposed a plan of conservation in 1990. In Amami-Oshima Island, the Amami Wildlife Conservation Center of the Ministry of the Environment was established in 1999. It designated the Amami rabbit as endangered in 2004 for Japan and restarted a mongoose eradication program in 2005.
References
External links
ARKive – images and movies of the Amami rabbit (Pentalagus furnessi)
Leporidae
Endemic mammals of Japan
Endemic fauna of the Ryukyu Islands
EDGE species
Mammals described in 1900 | Amami rabbit | [
"Biology"
] | 1,580 | [
"EDGE species",
"Biodiversity"
] |
341,089 | https://en.wikipedia.org/wiki/Ingeo | Ingeo is a range of polylactic acid (PLA) biopolymers owned by NatureWorks. Resinex Group distributes Ingeo in Europe.
Ingeo is created using carbon stored in plants via photosynthesis and takes the form of dextrose sugar. These sugars are then converted into a biopolymer through the processes of fermentation and separation. The resulting resin can then be injection molded into plastic goods, extruded for film applications, thermoformed into packaging, or extruded for use in textiles. However, its use in textiles is limited because of its limited comfort properties. Due to its biodegradability, PLA is applied in geotextiles, where the objective is that the material over time disappears.
PLA is more resistant to ultraviolet light than some synthetic plastics and has relatively low flammability. Due to its relatively higher hydrophobic character compared to the common polyester fibers, Ingeo is often blended with cotton and wool. This blend of materials results in lighter garments that can repel more moisture. PLA can be disposed of in the biological waste stream. In addition, like most polyesters, it can be recycled.
Ingeo is also used in packaging and plastic bottles. Its appearance can range from clear to opaque, and it can be flexible or rigid. The biopolymer is similar to polystyrene in exhibiting tensile strength and modulus comparable to hydrocarbon-based thermoplastics. Much like polyester, it resists grease and oil. Similarly, it also offers a flavor and odor barrier. Ingeo provides heat seal-ability at temperatures equivalent to those of polyolefin sealant resins.
See also
Bioplastics
Biodegradable plastic
References
Synthetic fibers | Ingeo | [
"Chemistry"
] | 366 | [
"Synthetic materials",
"Synthetic fibers"
] |
341,094 | https://en.wikipedia.org/wiki/List%20of%20placental%20mammals | The class Mammalia (mammals) is divided into two subclasses based on reproductive techniques: monotremes, which lay eggs, and therians, mammals which give live birth, which has two infraclasses: marsupials/metatherians and placentals/eutherians. See List of monotremes and marsupials, and for the clades and families, see Mammal classification. Classification updated from the VertLife website.
Magnorder Atlantogenata
Superorder Afrotheria
Grandorder Afroinsectiphilia
Order Tubulidentata (aardvarks)
Family Orycteropodidae
Genus Orycteropus
Aardvark, Orycteropus afer
Mirorder Afroinsectivora
Order Macroscelidea (elephant shrews)
Order Afrosoricida (tenrecs, golden moles and otter shrews)
Grandorder Paenungulata
Order Hyracoidea (hyraxes)
Family Procaviidae
Genus Dendrohyrax
Southern tree hyrax, Dendrohyrax arboreus
Western tree hyrax, Dendrohyrax dorsalis
Genus Heterohyrax
Yellow-spotted rock hyrax, Heterohyrax brucei
Genus Procavia
Cape hyrax, Procavia capensis
Mirorder Tethytheria
Order Proboscidea (elephants)
Family Elephantidae
Genus Loxodonta
African forest elephant, Loxodonta cyclotis
African bush elephant, Loxodonta africana
Genus Elephas
Asian elephant, Elephas maximus
Order Sirenia (dugongs and manatees)
Family Dugongidae
Genus Dugong
Dugong, Dugong dugon
Genus Hydrodamalis
†Steller's sea cow, Hydrodamalis gigas
Family Trichechidae
Genus Trichechus (manatees)
West Indian manatee, Trichechus manatus
African manatee, Trichechus senegalensis
Amazonian manatee, Trichechus inunguis
Dwarf manatee, Trichecus pygmaeus – validity questionable
Superorder Xenarthra
Order Cingulata (armadillos)
Order Pilosa (sloths and anteaters)
Magnorder Boreoeutheria
Superorder Euarchontoglires
Grandorder Euarchonta
Order Scandentia (treeshrews)
Mirorder Primatomorpha
Order Dermoptera (colugos)
Family Cynocephalidae
Genus Cynocephalus
Philippine flying lemur, Cynocephalus volans
Genus Galeopterus
Sunda flying lemur, Galeopterus variegatus
Order Primates
Grandorder Glires
Order Rodentia (mice, rats, etc.)
Order Lagomorpha (hares, rabbits, and pikas)
Superorder Laurasiatheria
Order Eulipotyphla (hedgehogs, moles, shrews, etc.)
Order Chiroptera (bats)
Grandorder Ferungulata
Mirorder Ferae
Order Pholidota (pangolins)
Order Carnivora
Mirorder Euungulata
Order Perissodactyla (odd-toed ungulates)
Order Artiodactyla (even-toed ungulates)
See also
Mammal classification
List of prehistoric mammals
List of recently extinct mammals
List of monotremes and marsupials
References
Taxonomic lists | List of placental mammals | [
"Biology"
] | 718 | [
"Lists of biota",
"Taxonomy (biology)",
"Taxonomic lists"
] |
341,107 | https://en.wikipedia.org/wiki/Ersatz%20good | An ersatz good () is a substitute good, especially one that is considered inferior to the good it replaces. It has particular connotations of wartime usage.
Etymology
Ersatz is a German word meaning substitute or replacement. Although it is used as an adjective in English, it is a noun in German. In German orthography noun phrases formed are usually represented as a single word, forming compound nouns such as Ersatzteile ("spare parts") or Ersatzspieler ("substitute player"). While ersatz in English generally means that the substitution is of unsatisfactory or inferior quality compared with the "real thing", in German, there is no such implication: e.g., Ersatzteile 'spare parts' is a technical expression without any implication about quality, Kaffeeersatz 'coffee substitute' is a drink from something other than coffee beans, and Ersatzzug 'replacement train' performs a comparable service. The term for inferior substitute in German would be Surrogat, which is cognate to the English word "surrogate".
Historical examples
World War I
In the opening months of World War I, replacement troops for battle-depleted German infantry units were drawn from lesser-trained Ersatz Corps, which were less effective than the troops they replaced.
Another example of the word's usage in Germany exists in the German naval construction programs at the beginning of the 20th century. In this context, the phrasing "Ersatz (ship name)" indicates that a new, larger or more capable ship was a replacement for an ageing or lost vessel. Because German practice was not to reveal the name of a new ship until its launch, this meant that the ship was known by its "Ersatz (ship name)" throughout its construction. At the end of World War I, the last three ships of the planned of battlecruisers were redesigned and initially known simply as the , since the first ship was considered to be a replacement for the lost armored cruiser .
The Allied naval blockade of Germany limited maritime commerce with Germany, forcing Germany and Austria-Hungary to develop substitutes for products such as chemical compounds and provisions. More than 11,000 ersatz products were sold in Germany during the war. Patents for ersatz products were granted for 6000 varieties of beer, wine and lemonade; 1000 kinds of soup cubes; 837 types of sausage and 511 assortments of coffee.
Ersatz products developed in Germany and Austria-Hungary during this time included:
synthetic rubber Kautschuk produced from petroleum for rubber
benzene for heating oil (coal gas)
industrial lubricants made by extracting oils from coal tar and brown-coal slags
synthetic camphor for imported natural camphor
nitrate crepe paper made from cellulose for gun cotton
glycerin from sugar rather than fats
gypsum-yielded sulphur
pigeon guano used to make fertilizer
flowers and weeds processed to make alcohol for ammunition
rosins and gums extracted from coal derivatives
tea composed of roasted barley, grasses, wild flowers, ground raspberry leaves or catnip
coffee substitute using roasted acorns, chicory and beechnuts (stretched with caramel-flavoured raw sugar and beet flower later in the war)
butter replaced by curdled milk, sugar and food colouring
cooking oil replaced by a mixture of beets, carrots, turnips and spices
salad oil was 99% mucilage
eggs replaced by yellow-coloured corn or potato flour
ground European beetles (cockchafers) and linden wood replaced fats
sausage made of water, plant fibres, animal scraps and blood (the infamous 'war sausage' which was equated to 'a mouthful of sawdust')
bouillon cubes made 70–90% of salt rather than meat extract
wheat flour stretched by adding potato flour and powdered hay
chocolates and cocoa replaced by ground cocoa shells and mixed pure pepper
oil and sunflower 'cakes' replaced corn and oats as horse feed
rapeseed, poppy and mustard 'cakes' replaced green feed for cattle
paper, peat, reeds, bulrushes and free-growing stinging nettle fibres replaced cotton in textiles
wood and paper used for shoe soles
Germany also stretched its supply of petrol with 'gasohol' (Benzolspiritus), which by today's standards would be classed as E25 petrol, consisting of 75% petrol and 25% distilled alcohol, likely ethanol.
World War II
In World War II, Ersatzbrot (substitute bread) made of potato starch, frequently stretched with extenders such as sawdust, was furnished to soldiers as Kommissbrot, a dark German bread baked from rye and other flours used for military rations, and also to prisoners of war. One recipe reportedly discovered in the "Food Providing Ministry" (Reichsnährstand) in Berlin, labeled "(Top Secret) Berlin 24.X1 1941", contained 50% bruised rye grain, 20% sliced sugar beets, 20% "tree flour" (sawdust), and 10% minced leaves and straw.
During the siege of Leningrad, its citizens were given ersatz flour instead of actual wheat flour (of which there was an extremely limited supply then) by the Soviet authorities. The lack of proper food with any nutrition meant that the city residents not only starved but became vulnerable to deadly illnesses and diseases (such as dysentery) owing to their weakened physical conditions. As a result, the word ersatz entered as a pejorative into Russian and other Slavic languages.
In Britain, this was additionally popularised as an adjective from the experiences of thousands of U.S., British, and other English-speaking combat personnel, primarily airmen, who were captured in the European Theater of Operations during World War II. These Allied prisoners of war were given ersatz goods such as Ersatzkaffee, an inferior Getreidekaffee or "grain coffee" as a coffee substitute by their German captors.
Eastern Bloc
In the Eastern Bloc, many agricultural goods could not be produced domestically, such as tea, coffee, nuts, and citrus fruits. These were generally imported from abroad with scarce foreign currency reserves, or inferior substitutes were produced domestically. In 1977, the East German coffee crisis resulted in the introduction of many coffee substitutes, which were generally rejected by the population. Replacements for orangeat and succade were made from candied carrot and unripe tomatoes.
Other
A study of conditions in the Southern United States during the United States Civil War is called Ersatz in the Confederacy.
Effectiveness
When presented with a choice of ersatz, one tends to prefer the generic version of the name brand rather than an entirely different product. Specifically one that most closely resembles the original and meets the same goal.
For instance, a person who desires a gourmet chocolate is more likely to choose another, less expensive chocolate as a substitute than a different kind of dessert or snack. Because such "within-category" substitutes are easier to compare to the desired good, however, those that are inferior are less effective than "cross-category" substitutes that fulfill the same goal. People are more able to notice their inferiority during consumption, which leads them to be less satisfying than goal-derived substitutes from different taxonomic categories.
During the First World War in Germany and Austria-Hungary, people succumbed to sickness from the consumption of ersatz goods. In Austria, the term "Vienna sickness" was coined after malnutrition from such goods was linked to a cause of the tuberculosis epidemic (10,000 reported cases).
In Germany, Princess Blücher suffered from influenza in 1916, suggesting that she was suffering from "ersatz illness". She writes: "everyone is feeling ill from too many chemicals in the hotel food. I don't believe that Germany will ever be starved out, but she will be poisoned out first with these substitutes."
See also
Adulterant
Austerity
Backstop resources
Claytons, a word used in Australian and New Zealand English
Counterfeit
Giffen good, a good for which there is no ersatz replacement, causing demand to rise with prices
References
German words and phrases
Goods (economics)
Imitation foods
Perfect competition
Survival skills | Ersatz good | [
"Physics"
] | 1,710 | [
"Materials",
"Goods (economics)",
"Matter"
] |
341,115 | https://en.wikipedia.org/wiki/Fish%20ladder | A fish ladder, also known as a fishway, fish pass, fish steps, or fish cannon, is a structure on or around artificial and natural barriers (such as dams, locks and waterfalls) to facilitate diadromous fishes' natural migration as well as movements of potamodromous species. Most fishways enable fish to pass around the barriers by swimming and leaping up a series of relatively low steps (hence the term ladder) into the waters on the other side. The velocity of water falling over the steps has to be great enough to attract the fish to the ladder, but it cannot be so great that it washes fish back downstream or exhausts them to the point of inability to continue their journey upriver.
History
Written reports of rough fishways date to 17th-century France, where bundles of branches were used to make steps in steep channels to bypass obstructions.
A 1714 construction of an old channel bypassing a dam, "originally cut for the passage of fish up and down the river", is mentioned in the 1823 U.S. Circuit Court Case Tyler v. Wilkinson. This example predates the 1880 fish ladder at Pawtuxet Falls. The 1714 channel "wholly failed for this purpose" and, in 1730, a mill was built in its place. The channel and its mill usage became an important legal case in U.S. water law.
A pool and weir salmon ladder was built around 1830 by James Smith, a Scottish engineer on the River Teith, near Deanston, Perthshire in Scotland. Both the weir and salmon ladder are there today and many subsequent salmon ladders built in Scotland were inspired by it.
A version was patented in 1837 by Richard McFarlan of Bathurst, New Brunswick, Canada, who designed a fishway to bypass a dam at his water-powered lumber mill. In 1852–1854, the Ballisodare Fish Pass was built in County Sligo in Ireland to draw salmon into a river that had not supported a fishery. In 1880, the first fish ladder was built in Rhode Island, United States, on the Pawtuxet Falls Dam. The ladder was removed in 1924, when the City of Providence replaced the wood dam with a concrete one. USA legislated fishways in 1888.
As the Industrial Age advanced, dams and other river obstructions became larger and more common, leading to the need for effective fish by-passes.
Types
Pool and weir One of the oldest styles of fish ladders. It uses a series of small dams and pools of regular length to make a long, sloping channel for fish to travel around the obstruction. The channel acts as a fixed lock to gradually step down the water level; to head upstream, fish must jump over from box to box in the ladder.
Baffle fishway Uses a series of symmetrical close-spaced baffles in a channel to redirect the flow of water, allowing fish to swim around the barrier. Baffle fishways need not have resting areas, although pools can be included to provide a resting area or to reduce the velocity of the flow. Such fishways can be built with switchbacks to minimize the space needed for their construction. Baffles come in variety of designs. The most common design is the Larinier pass, named after the French engineer who designed them. They are suitable for coarse fish as well as salmonids, and can be built large enough to be used by canoes. The original design for a Denil fishway was developed in 1909 by a Belgian scientist, G. Denil; it has since been adjusted and adapted in many ways. The Alaskan Steeppass, for example, is a modular prefabricated Denil-fishway variant originally designed for remote areas of Alaska. Baffles have been installed by Project Maitai in several waterways in Nelson, New Zealand, to improve fish passage as part of general environmental restoration.
Fish elevator (or fish lift) Breaks with the ladder design by providing a sort of elevator to carry fish over a barrier. It is well suited to tall barriers. With a fish elevator, fish swim into a collection area at the base of the obstruction. When enough fish accumulate in the collection area, they are nudged into a hopper that carries them into a flume that empties into the river above the barrier. On the Connecticut River, for example, two fish elevators lift up to 500 fish at a time, 52 feet (15.85 m), to clear the Holyoke Dam. In 2013, the elevator carried over 400,000 fish.
Rock-ramp fishway Uses large rocks and timbers to make pools and small falls that mimic natural structures. Because of the length of the channel needed for the ladder, such structures are most appropriate for relatively short barriers. They have a significant advantage in that they can provide fish spawning habitat.
Vertical-slot fish passage Similar to a pool-and-weir system, except that each "dam" has a narrow slot in it near the channel wall. This allows fish to swim upstream without leaping over an obstacle. Vertical-slot fish passages also tend to handle reasonably well the seasonal fluctuation in water levels on each side of the barrier. Recent studies suggest that navigation locks have a potential to be operated as vertical slot fishways to provide increased access for a range of biota, including poor swimmers.
Fish siphon Allows the pass to be installed parallel to a water course and can be used to link two watercourses. The pass utilises a syphon effect to regulate its flow. This style is particularly favoured to aid flood defence.
Fish cannon A wet, flexible pneumatic tube uses air pressure to suck in salmon one at a time and gently shoot them out into the destination water. The system was originally designed by Bellevue, Washington company Whooshh to safely move apples.
Fish lock A fish lock is a structure designed to facilitate the passage of fish over barriers such as dams or weirs, enabling them to access upstream habitats essential for spawning and growth. It operates similarly to a navigation lock, using a chamber that fills and empties to move fish across the barrier by adjusting water levels to match the upstream and downstream sections. There are several types of fish locks, such as the Borland fish lock, Deelder lock, Pavlov lock, and most recently, the Fishcon lock.
Fishcon lock The Fishcon lock enables both upstream and downstream fish migration in a compact space and was developed by the company Fishcon. Between 2019 and mid-2024, seven Fishcon locks were installed in Austria, Germany and Switzerland. Five of these installations have been already independently evaluated with great results and deemed functional according to Austrian and German standards.
Borland fish lock This is similar to a canal lock. At the downstream end of the obstruction, fish are attracted to a collecting pool by an outflow of water through a sluice gate. At fixed intervals, the gate is closed, and water from the upper level fills the collecting pool and an inclined shaft, lifting the fish up to the upstream level. Once the shaft is full, a sluice at the top level opens, to allow fish to continue their journey upstream. The top sluice then closes, and the shaft empties for the process to begin again. A number of Borland fish locks have been built in Scotland, associated with hydro-electric dams, including one at Aigas Dam on the River Beauly.
Deelder lock Developed by Dutch engineer Klaas Deelder, this design features two chambers separated by an internal weir. Fish enter the lower chamber, which then fills with water, allowing them to swim over the weir into the upper chamber and continue upstream. This method has been effective in passing a wide range of fish species and sizes.
Pavlov lock This design, attributed to Russian engineer Dmitry Sergeyevich Pavlov, incorporates features to guide fish into the lock chamber, such as attraction flows and holding pools. The lock operates cyclically, filling and emptying to move fish upstream, and has been implemented in various regions to assist fish migration.
Effectiveness
Fish ladders have a mixed record of effectiveness. This varies for different types of species, with one study showing that only three percent of American Shad make it through all the fish ladders on the way to their spawning ground. Effectiveness depends on the fish species' swimming ability, and how the fish moves up and downstream. A fish passage that is designed to allow fish to pass upstream may not allow passage downstream, for instance. Fish passages do not always work.
In practice a challenge is matching swimming performance data to hydrodynamic measurements. Swim tests rarely use the same protocol and the output is either a single-point measurement or a bulk velocity. In contrast, physical and numerical modelling of fluid flow (i.e. hydrodynamics) deliver a detailed flow map, with a fine spatial and temporal resolution. Regulatory agencies face a difficult task to match hydrodynamic measurements and swimming performance data.
Culverts
During the last three decades, the ecological impact of culverts on natural streams and rivers has been recognised. While the culvert discharge capacity derives from hydrological and hydraulic engineering considerations, this results often in large velocities in the barrel, which may prevent fish from passing through.
Baffles may be installed along the barrel invert to provide some fish-friendly alternative. For low discharges, the baffles decrease the flow velocity and increase the water depth to facilitate fish passage. At larger discharges, baffles induce lower local velocities and generate recirculation regions. However, baffles can reduce drastically the culvert discharge capacity for a given afflux, thus increasing substantially the total cost of the culvert structure to achieve the same design discharge and afflux. It is believed that fish-turbulence interplay may facilitate upstream migration, albeit an optimum design must be based upon a careful characterisation of both hydrodynamics and fish kinematics. Finally the practical engineering design implications cannot be ignored, while a solid understanding of turbulence typology is a basic requirement to any successful boundary treatment conducive of upstream fish passage.
See also
Citations
General and cited references
To Save the Salmon (1997) US Army Corps of Engineers.
Fish-friendly waterways and culverts - Integration of hydrodynamics and fish turbulence interplay (2017) The University of Queensland.
External links
A study of the hydraulics of flow over fishways
Construction of a vertical slot fish passage and eel ladder for the St. Ours Dam (Richelieu River, Québec)
Fish Passage Center
Fish passes. Design, dimensions and monitoring, Food and Agriculture Organization of the United Nations/Deutscher Verband für Wasserwirtschaft und Kulturbau (DVWK), Rome, 2002 (Zip download from FTP area of the FAO's European Inland Fisheries Advisory Commission (EIFAC))
U.S. Orders Modification of Klamath River – Dams Removal May Prove More Cost-Effective for allowing the passage of Salmon—The Washington Post, January 31, 2007
Fish Ladders and Elevators not working.
Upstream fish passage in box culverts: how do fish and turbulence interplay? by Dr Hang Wang and Professor Hubert Chanson, School of Civil Engineering, University of Queensland
Aquatic ecology
Ecological connectivity
Fish migrations | Fish ladder | [
"Biology"
] | 2,305 | [
"Aquatic ecology",
"Ecosystems"
] |
341,127 | https://en.wikipedia.org/wiki/List%20of%20functional%20analysis%20topics | This is a list of functional analysis topics.
See also: Glossary of functional analysis.
Hilbert space
Functional analysis, classic results
Operator theory
Banach space examples
Lp space
Hardy space
Sobolev space
Tsirelson space
ba space
Real and complex algebras
Topological vector spaces
Amenability
Amenable group
Von Neumann conjecture
Wavelets
Quantum theory
See also list of mathematical topics in quantum theory
Probability
Free probability
Bernstein's theorem
Non-linear
Fixed-point theorems in infinite-dimensional spaces
History
Stefan Banach (1892–1945)
Hugo Steinhaus (1887–1972)
John von Neumann (1903-1957)
Alain Connes (born 1947)
Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis
Earliest Known Uses of Some of the Words of Mathematics: Matrices and Linear Algebra
Functional analysis | List of functional analysis topics | [
"Mathematics"
] | 161 | [
"Functional analysis",
"Functions and mappings",
"Mathematical relations",
"Mathematical objects"
] |
341,133 | https://en.wikipedia.org/wiki/Induction%20welding | Induction welding is a form of welding that uses electromagnetic induction to heat the workpiece. The welding apparatus contains an induction coil that is energised with a radio-frequency electric current. This generates a high-frequency electromagnetic field that acts on either an electrically conductive or a ferromagnetic workpiece. In an electrically conductive workpiece, the main heating effect is resistive heating, which is due to induced currents called eddy currents. In a ferromagnetic workpiece, the heating is caused mainly by hysteresis, as the electromagnetic field repeatedly distorts the magnetic domains of the ferromagnetic material. In practice, most materials undergo a combination of these two effects.
Nonmagnetic materials and electrical insulators such as plastics can be induction-welded by implanting them with metallic or ferromagnetic compounds, called susceptors, that absorb the electromagnetic energy from the induction coil, become hot, and lose their heat to the surrounding material by thermal conduction.
Plastic can also be induction welded by embedding the plastic with electrically conductive fibers like metals or carbon fiber. Induced eddy currents resistively heat the embedded fibers which lose their heat to the surrounding plastic by conduction. Induction welding of carbon fiber reinforced plastics is commonly used in the aerospace industry.
Induction welding is used for long production runs and is a highly automated process, usually used for welding the seams of pipes. It can be a very fast process, as a lot of power can be transferred to a localised area, so the faying surfaces melt very quickly and can be pressed together to form a continuous rolling weld.
The depth that the currents, and therefore heating, penetrates from the surface is inversely proportional to the square root of the frequency. The temperature of the metals being welded and their composition will also affect the penetration depth. This process is very similar to resistance welding, except that in the case of resistance welding the current is delivered using contacts to the workpiece instead of using induction.
Induction welding was first discovered by Michael Faraday. The basics of induction welding explain that the magnetic field's direction is dependent on the direction of current flow. and the field's direction will change at the same rate as the current's frequency. For example, a 120 Hz AC current will cause the field to change directions 120 times a second. This concept is known as Faraday's Law.
When induction welding takes place, the work pieces heat up to under the melting temperature and the edges of the pieces are placed together impurities get forced out to give a solid forge weld.
Induction welding is used for joining a multitude of thermoplastics and thermosetting matrix composites. The apparatus used for induction welding processes includes a radio frequency power generator, a heating station, the work piece material, and a cooling system.
The power generator comes in either the form of solid state or vacuum tube and is used to provide an alternating current of 230-340 V or a frequency of 50–60 Hz to the system. This value is determined by what induction coil is used with the piece.
The heat station utilizes a capacitor and a coil to heat the work pieces. The capacitor matches the power generators output and the induction coil transfers energy to the piece. When welding the coil needs to be close to the work piece to maximize the energy transfer and the work piece used during induction welding is an important key component of optimal efficiency.
Some equations to consider for induction welding include:
Thermal calculation:
Where: is thermal mass
is resistivity
is efficiency
is surface density
Newton Cooling Equation:
Where: is heat flux density
h is the heat transfer coefficient
is the temperature of the work piece surface
is the temperature of the surrounding air
See also
Induction heating
Implant induction welding of thermoplastics
References
AWS Welding Handbook, Volume 2, 8th Edition
.
Welding | Induction welding | [
"Engineering"
] | 790 | [
"Welding",
"Mechanical engineering"
] |
341,149 | https://en.wikipedia.org/wiki/Matrix%20similarity | In linear algebra, two n-by-n matrices and are called similar if there exists an invertible n-by-n matrix such that
Similar matrices represent the same linear map under two (possibly) different bases, with being the change-of-basis matrix.
A transformation is called a similarity transformation or conjugation of the matrix . In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however, in a given subgroup of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that be chosen to lie in .
Motivating example
When defining a linear transformation, it can be the case that a change of basis can result in a simpler form of the same transformation. For example, the matrix representing a rotation in when the axis of rotation is not aligned with the coordinate axis can be complicated to compute. If the axis of rotation were aligned with the positive -axis, then it would simply be
where is the angle of rotation. In the new coordinate system, the transformation would be written as
where and are respectively the original and transformed vectors in a new basis containing a vector parallel to the axis of rotation. In the original basis, the transform would be written as
where vectors and and the unknown transform matrix are in the original basis. To write in terms of the simpler matrix, we use the change-of-basis matrix that transforms and as and :
Thus, the matrix in the original basis, , is given by . The transform in the original basis is found to be the product of three easy-to-derive matrices. In effect, the similarity transform operates in three steps: change to a new basis (), perform the simple transformation (), and change back to the old basis ().
Properties
Similarity is an equivalence relation on the space of square matrices.
Because matrices are similar if and only if they represent the same linear operator with respect to (possibly) different bases, similar matrices share all properties of their shared underlying operator:
Rank
Characteristic polynomial, and attributes that can be derived from it:
Determinant
Trace
Eigenvalues, and their algebraic multiplicities
Geometric multiplicities of eigenvalues (but not the eigenspaces, which are transformed according to the base change matrix P used).
Minimal polynomial
Frobenius normal form
Jordan normal form, up to a permutation of the Jordan blocks
Index of nilpotence
Elementary divisors, which form a complete set of invariants for similarity of matrices over a principal ideal domain
Because of this, for a given matrix A, one is interested in finding a simple "normal form" B which is similar to A—the study of A then reduces to the study of the simpler matrix B. For example, A is called diagonalizable if it is similar to a diagonal matrix. Not all matrices are diagonalizable, but at least over the complex numbers (or any algebraically closed field), every matrix is similar to a matrix in Jordan form. Neither of these forms is unique (diagonal entries or Jordan blocks may be permuted) so they are not really normal forms; moreover their determination depends on being able to factor the minimal or characteristic polynomial of A (equivalently to find its eigenvalues). The rational canonical form does not have these drawbacks: it exists over any field, is truly unique, and it can be computed using only arithmetic operations in the field; A and B are similar if and only if they have the same rational canonical form. The rational canonical form is determined by the elementary divisors of A; these can be immediately read off from a matrix in Jordan form, but they can also be determined directly for any matrix by computing the Smith normal form, over the ring of polynomials, of the matrix (with polynomial entries) (the same one whose determinant defines the characteristic polynomial). Note that this Smith normal form is not a normal form of A itself; moreover it is not similar to either, but obtained from the latter by left and right multiplications by different invertible matrices (with polynomial entries).
Similarity of matrices does not depend on the base field: if L is a field containing K as a subfield, and A and B are two matrices over K, then A and B are similar as matrices over K if and only if they are similar as matrices over L. This is so because the rational canonical form over K is also the rational canonical form over L. This means that one may use Jordan forms that only exist over a larger field to determine whether the given matrices are similar.
In the definition of similarity, if the matrix P can be chosen to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent. The spectral theorem says that every normal matrix is unitarily equivalent to some diagonal matrix. Specht's theorem states that two matrices are unitarily equivalent if and only if they satisfy certain trace equalities.
See also
Canonical forms
Matrix congruence
Matrix equivalence
Jacobi rotation
References
Citations
General references
(Similarity is discussed many places, starting at page 44.)
Matrices
Equivalence (mathematics) | Matrix similarity | [
"Mathematics"
] | 1,077 | [
"Matrices (mathematics)",
"Mathematical objects"
] |
341,265 | https://en.wikipedia.org/wiki/Jungle | A jungle is land covered with dense forest and tangled vegetation, usually in tropical climates. Application of the term has varied greatly during the past century.
Etymology
The word jungle originates from the Sanskrit word jaṅgala (), meaning rough and arid. It came into the English language in the 18th century via the Hindustani word for forest (Hindi/Urdu: /) (Jangal). Jāṅgala has also been variously transcribed in English as jangal, jangla, jungal, and juṅgala.
It has been suggested that an Anglo-Indian interpretation led to its connotation as a dense "tangled thicket". The term is prevalent in many languages of the Indian subcontinent, and the Iranian Plateau, where it is commonly used to refer to the plant growth replacing primeval forest or to the unkempt tropical vegetation that takes over abandoned areas.
Wildlife
Because jungles occur on all inhabited landmasses and may incorporate numerous vegetation and land types in different climatic zones, the wildlife of jungles cannot be straightforwardly defined.
Varying usage
As dense and tangled vegetation
One of the most common meanings of jungle is land overgrown with tangled vegetation at ground level, especially in the tropics. Typically such vegetation is sufficiently dense to hinder movement by humans, requiring that travellers cut their way through. This definition draws a distinction between rainforest and jungle, since the understorey of rainforests is typically open of vegetation due to a lack of sunlight, and hence relatively easy to traverse. Jungles may exist within, or at the borders of, tropical forests in areas where the woodland has been opened through natural disturbance such as hurricanes, or through human activity such as logging. The successional vegetation that springs up following such disturbance, is dense and tangled and is a "typical" jungle. Jungle also typically forms along rainforest margins such as stream banks, once again due to the greater available light at ground level.
Monsoon forests and mangroves are commonly referred to as jungles of this type. Having a more open canopy than rainforests, monsoon forests typically have dense understoreys with numerous lianas and shrubs making movement difficult, while the prop roots and low canopies of mangroves produce similar difficulties.
As moist forest
Because European explorers initially travelled through tropical forests largely by river, the dense tangled vegetation lining the stream banks gave a misleading impression that such jungle conditions existed throughout the entire forest. As a result, it was wrongly assumed that the entire forest was impenetrable jungle. This in turn appears to have given rise to the second popular usage of jungle as virtually any humid tropical forest. Jungle in this context is particularly associated with tropical rain forest, but may extend to cloud forest, temperate rainforest, and mangroves with no reference to the vegetation structure or the ease of travel.
The terms "tropical forest" and "rainforest" have largely replaced "jungle" as the descriptor of humid tropical forests, a linguistic transition that has occurred since the 1970s. "Rainforest" itself did not appear in English dictionaries prior to the 1970s. The word "jungle" accounted for over 80% of the terms used to refer to tropical forests in print media prior to the 1970s; since then it has been steadily replaced by "rainforest", although "jungle" still remains in common use when referring to tropical rainforests.
As metaphor
As a metaphor, jungle often refers to situations that are unruly or lawless, or where the only law is perceived to be "survival of the fittest". This reflects the view of "city people" that forests are such places. Upton Sinclair gave the title The Jungle (1906) to his famous book about the life of workers at the Chicago Stockyards, portraying the workers as being mercilessly exploited with no legal or other lawful recourse.
The term "The Law of the Jungle" is also used in a similar context, drawn from Rudyard Kipling's The Jungle Book (1894)—though in the society of jungle animals portrayed in that book and obviously meant as a metaphor for human society, that phrase referred to an intricate code of laws which Kipling describes in detail, and not at all to a lawless chaos.
The word "jungle" carries connotations of untamed and uncontrollable nature and isolation from civilisation, along with the emotions that evokes: threat, confusion, powerlessness, disorientation and immobilisation. The change from "jungle" to "rainforest" as the preferred term for describing tropical forests has been a response to an increasing perception of these forests as fragile and spiritual places, a viewpoint not in keeping with the darker connotations of "jungle".
Cultural scholars, especially post-colonial critics, often analyse the jungle within the concept of hierarchical domination and the demand western cultures often places on other cultures to conform to their standards of civilisation. For example: Edward Said notes that the Tarzan depicted by Johnny Weissmuller was a resident of the jungle representing the savage, untamed and wild, yet still a white master of it; and in his essay "An Image of Africa" about Heart of Darkness Nigerian novelist and theorist Chinua Achebe notes how the jungle and Africa become the source of temptation for white European characters like Marlowe and Kurtz.
Former Israeli Prime Minister Ehud Barak compared Israel to "a villa in the jungle", a comparison which had been often quoted in Israeli political debates. Barak's critics on the left side of Israeli politics strongly criticised the comparison.
See also
Monsoon forest
Arid Forest Research Institute (AFRI)
Rainforest
Wilderness
Grove (nature)
Amazon rainforest
References
External links
BBC - Science and Nature: Jungle
"Biomes of the World" by Dennis Paulson
Forests
Metaphors
Landscape | Jungle | [
"Biology"
] | 1,158 | [
"Forests",
"Ecosystems"
] |
341,393 | https://en.wikipedia.org/wiki/Laplace%20number | The Laplace number (), also known as the Suratman number (), is a dimensionless number used in the characterization of free surface fluid dynamics. It represents a ratio of surface tension to the momentum-transport (especially dissipation) inside a fluid. It is named after Pierre-Simon Laplace and Indonesian physicist P. C. Suratman.
It is defined as follows:
where:
σ = surface tension
ρ = density
L = length
μ = liquid viscosity
Laplace number is related to Reynolds number (Re) and Weber number (We) in the following way:
See also
Ohnesorge number - There is an inverse relationship, , between the Laplace number and the Ohnesorge number.
References
Dimensionless numbers of fluid mechanics
Fluid dynamics | Laplace number | [
"Chemistry",
"Engineering"
] | 161 | [
"Piping",
"Chemical engineering",
"Fluid dynamics"
] |
341,394 | https://en.wikipedia.org/wiki/The%20Analyst | The Analyst (subtitled A Discourse Addressed to an Infidel Mathematician: Wherein It Is Examined Whether the Object, Principles, and Inferences of the Modern Analysis Are More Distinctly Conceived, or More Evidently Deduced, Than Religious Mysteries and Points of Faith) is a book by George Berkeley. It was first published in 1734, first by J. Tonson (London), then by S. Fuller (Dublin). The "infidel mathematician" is believed to have been Edmond Halley, though others have speculated Sir Isaac Newton was intended.
The book contains a direct attack on the foundations of calculus, specifically on Isaac Newton's notion of fluxions and on Leibniz's notion of infinitesimal change.
Background and purpose
From his earliest days as a writer, Berkeley had taken up his satirical pen to attack what were then called 'free-thinkers' (secularists, sceptics, agnostics, atheists, etc.—in short, anyone who doubted the truths of received Christian religion or called for a diminution of religion in public life). In 1732, in the latest installment in this effort, Berkeley published his Alciphron, a series of dialogues directed at different types of 'free-thinkers'. One of the archetypes Berkeley addressed was the secular scientist, who discarded Christian mysteries as unnecessary superstitions, and declared his confidence in the certainty of human reason and science. Against his arguments, Berkeley mounted a subtle defense of the validity and usefulness of these elements of the Christian faith.
Alciphron was widely read and caused a bit of a stir. But it was an offhand comment mocking Berkeley's arguments by the 'free-thinking' royal astronomer Sir Edmund Halley that prompted Berkeley to pick up his pen again and try a new tack. The result was The Analyst, conceived as a satire attacking the foundations of mathematics with the same vigour and style as 'free-thinkers' routinely attacked religious truths.
Berkeley sought to take apart the then foundations of calculus, claimed to uncover numerous gaps in proof, attacked the use of infinitesimals, the diagonal of the unit square, the very existence of numbers, etc. The general point was not so much to mock mathematics or mathematicians, but rather to show that mathematicians, like Christians, relied upon incomprehensible 'mysteries' in the foundations of their reasoning. Moreover, the existence of these 'superstitions' was not fatal to mathematical reasoning, indeed it was an aid. So too with the Christian faithful and their 'mysteries'. Berkeley concluded that the certainty of mathematics is no greater than the certainty of religion.
Content
The Analyst was a direct attack on the foundations of calculus, specifically on Newton's notion of fluxions and on Leibniz's notion of infinitesimal change. In section 16, Berkeley criticises
...the fallacious way of proceeding to a certain Point on the Supposition of an Increment, and then at once shifting your Supposition to that of no Increment . . . Since if this second Supposition had been made before the common Division by o, all had vanished at once, and you must have got nothing by your Supposition. Whereas by this Artifice of first dividing, and then changing your Supposition, you retain 1 and nxn-1. But, notwithstanding all this address to cover it, the fallacy is still the same.
It is a frequently quoted passage, particularly when he wrote:
And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?
Berkeley did not dispute the results of calculus; he acknowledged the results were true. The thrust of his criticism was that Calculus was not more logically rigorous than religion. He instead questioned whether mathematicians "submit to Authority, take things upon Trust" just as followers of religious tenets did. According to Burton, Berkeley introduced an ingenious theory of compensating errors that were meant to explain the correctness of the results of calculus. Berkeley contended that the practitioners of calculus introduced several errors which cancelled, leaving the correct answer. In his own words, "by virtue of a twofold mistake you arrive, though not at science, yet truth."
Analysis
The idea that Newton was the intended recipient of the discourse is put into doubt by a passage that appears toward the end of the book:
"Query 58: Whether it be really an effect of Thinking, that the same Men admire the great author for his Fluxions, and deride him for his Religion?"
Here Berkeley ridicules those who celebrate Newton (the inventor of "fluxions", roughly equivalent to the differentials of later versions of the differential calculus) as a genius while deriding his well-known religiosity. Since Berkeley is here explicitly calling attention to Newton's religious faith, that seems to indicate he did not mean his readers to identify the "infidel (i.e., lacking faith) mathematician" with Newton.
Mathematics historian Judith Grabiner comments, "Berkeley's criticisms of the rigor of the calculus were witty, unkind, and — with respect to the mathematical practices he was criticizing — essentially correct". While his critiques of the mathematical practices were sound, his essay has been criticised on logical and philosophical grounds.
For example, David Sherry argues that Berkeley's criticism of infinitesimal calculus consists of a logical criticism and a metaphysical criticism. The logical criticism is that of a fallacia suppositionis, which means gaining points in an argument by means of one assumption and, while keeping those points, concluding the argument with a contradictory assumption. The metaphysical criticism is a challenge to the existence itself of concepts such as fluxions, moments, and infinitesimals, and is rooted in Berkeley's empiricist philosophy which tolerates no expression without a referent. Andersen (2011) showed that Berkeley's doctrine of the compensation of errors contains a logical circularity. Namely, Berkeley's determination of the derivative of the quadratic function relies on Apollonius's determination of the tangent of the parabola.
Influence
Two years after this publication, Thomas Bayes published anonymously "An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst" (1736), in which he defended the logical foundation of Isaac Newton's calculus against the criticism outlined in The Analyst. Colin Maclaurin's two-volume Treatise of Fluxions published in 1742 also began as a response to Berkeley attacks, intended to show that Newton's calculus was rigorous by reducing it to the methods of Greek geometry.
Despite these attempts, calculus continued to be developed using non-rigorous methods until around 1830 when Augustin Cauchy, and later Bernhard Riemann and Karl Weierstrass, redefined the derivative and integral using a rigorous definition of the concept of limit. The idea of using limits as a foundation for calculus had been suggested by d'Alembert, but d'Alembert's definition was not rigorous by modern standards. The concept of limits had already appeared in the work of Newton, but was not stated with sufficient clarity to hold up to the criticism of Berkeley.
In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting calculus on a mathematically rigorous foundation, the way it was done before the (ε, δ)-definition of limit had been fully developed.
Ghosts of departed quantities
Towards the end of The Analyst, Berkeley addresses possible justifications for the foundations of calculus that mathematicians may put forward. In response to the idea fluxions could be defined using ultimate ratios of vanishing quantities, Berkeley wrote:
It must, indeed, be acknowledged, that [Newton] used Fluxions, like the Scaffold of a building, as things to be laid aside or got rid of, as soon as finite Lines were found proportional to them. But then these finite Exponents are found by the help of Fluxions. Whatever therefore is got by such Exponents and Proportions is to be ascribed to Fluxions: which must therefore be previously understood. And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the Ghosts of departed Quantities?
Edwards describes this as the most memorable point of the book. Katz and Sherry argue that the expression was intended to address both infinitesimals and Newton's theory of fluxions.
Today the phrase "ghosts of departed quantities" is also used when discussing Berkeley's attacks on other possible foundations of Calculus. In particular it is used when discussing infinitesimals, but it is also used when discussing differentials, and adequality.
Text and commentary
The full text of The Analyst can be read on Wikisource, as well as on David R. Wilkins' website, which includes some commentary and links to responses by Berkeley's contemporaries.
The Analyst is also reproduced, with commentary, in recent works:
William Ewald's From Kant to Hilbert: A Source Book in the Foundations of Mathematics.
Ewald concludes that Berkeley's objections to the calculus of his day were mostly well taken at the time.
D. M. Jesseph's overview in the 2005 "Landmark Writings in Western Mathematics".
References
Sources
External links
1734 books
Books by George Berkeley
Mathematics books
History of calculus
Mathematics of infinitesimals
Isaac Newton
Freethought
Satirical books
Works about Gottfried Wilhelm Leibniz | The Analyst | [
"Mathematics"
] | 2,009 | [
"Mathematics of infinitesimals",
"History of calculus",
"Calculus"
] |
341,395 | https://en.wikipedia.org/wiki/Straw-bale%20construction | Straw-bale construction is a building method that uses bales of straw (usually wheat straw) as structural elements, building insulation, or both. This construction method is commonly used in natural building or "brown" construction projects. Research has shown that straw-bale construction is a sustainable method for building, from the standpoint of both materials and energy needed for heating and cooling.
Advantages of straw-bale construction over conventional building systems include the renewable nature of straw, cost, easy availability, naturally fire-retardant and high insulation value. Disadvantages include susceptibility to rot, difficulty of obtaining insurance coverage, and high space requirements for the straw itself. Research has been done using moisture probes placed within the straw wall in which 7 of 8 locations had moisture contents of less than 20%. This is a moisture level that does not aid in the breakdown of the straw. However, proper construction of the straw-bale wall is important in keeping moisture levels down, just as in the construction of any type of building.
History
Straw houses have been built on the African plains since the Paleolithic Era. Straw bales were used in construction 400 years ago in Germany; and straw-thatched roofs have long been used in northern Europe and Asia. When European Settlers came to North America, teepees were insulated in winter with loose straw between the inner lining and outer cover.
Straw-bale construction was greatly facilitated by the mechanical hay baler, which was invented in the 1850s and was widespread by the 1890s. It proved particularly useful in the Nebraska Sandhills. Pioneers seeking land under the 1862 Homestead Act and the 1904 Kinkaid Act found a dearth of trees over much of Nebraska. In many parts of the state, the soil was suitable for dugouts and sod houses.
However, in the Sandhills, the soil generally made poor construction sod;
in the few places where suitable sod could be found, it was more valuable for agriculture than as a building material.
The first documented use of hay bales in construction in Nebraska was a schoolhouse built in 1896 or 1897. Unfenced and unprotected by stucco or plaster, it was reported in 1902 as having been eaten by cows. To combat this, builders began plastering their bale structures; if cement or lime stucco was unavailable, locally obtained "gumbo mud" was employed. Between 1896 and 1945, an estimated 70 straw-bale buildings, including houses, farm buildings, churches, schools, offices, and grocery stores had been built in the Sandhills. In 1990, nine surviving bale buildings were reported in Arthur and Logan Counties,
including the 1928 Pilgrim Holiness Church in the village of Arthur, which is listed in the National Register of Historic Places.
Since the 1990s straw-bale construction has been substantially revived, particularly in North America, Europe, and Australia. Straw was one of the first materials to be used in green buildings. This revival is likely attributed to greater environmental awareness and the material's natural, non-toxic qualities, low embodied energy, and relative affordability. Straw-bale construction has encountered issues regarding building codes depending on the location of the building. However, in the USA, the introduction of Appendices S and R in the 2015 International Residential Code has helped to legitimize and improve understanding of straw-bale construction. In France, the approval in 2012 of professional rules for straw-building recognized it as “common technology” and qualifies for standard-insurance programs.
Method
Straw bale building typically consists of stacking rows of bales (often in running-bond) on a raised footing or foundation, with a moisture barrier or capillary break between the bales and their supporting platform. There are two types of straw-bales commonly used, those bound together with two strings and those with three. The three string bale is the larger in all three dimensions. Bale walls can be tied together with pins of bamboo or wood (internal to the bales or on their faces), or with surface wire meshes, and then stuccoed or plastered, either with a lime-based formulation or earth/clay render. The bales may actually provide the structural support for the building ("load-bearing" or "Nebraska-style" technique), as was the case in the original examples from the late 19th century. The plastered bale assembly also can be designed to provide lateral and shear support for wind and seismic loads.
Alternatively, bale buildings can have a structural frame of other materials, usually lumber or timber-frame, with bales simply serving as insulation and plaster substrate, ("infill" or "non-loadbearing" technique), which is most often required in northern regions and/or in wet climates. In northern regions, the potential snow-loading can exceed the strength of the bale walls. In wet climates, the imperative for applying a vapor-permeable finish precludes the use of cement-based stucco. Additionally, the inclusion of a skeletal framework of wood or metal allows the erection of a roof prior to raising the bales, which can protect the bale wall during construction, when it is the most vulnerable to water damage in all but the most dependably arid climates. A combination of framing and load-bearing techniques may also be employed, referred to as "hybrid" straw bale construction.
Straw bales can also be used as part of a Spar and Membrane Structure (SMS) wall system in which lightly reinforced sprayed concrete skins are interconnected with extended X-shaped light rebar in the head joints of the bales. In this wall system the concrete skins provide structure, seismic reinforcing, and fireproofing, while the bales are used as leave-in formwork and insulation.
The University of Bath has completed a research programme which used ‘ModCell’ panels—prefabricated panels consisting of a wooden structural frame infilled with straw bales and rendered with a breathable lime-based system—to build 'BaleHaus', a straw bale construction on the university's campus. Monitoring work of the structure carried out by architectural researchers at the university has found that as well as reducing the environmental footprint, the construction offers other benefits, including healthier living through higher levels of thermal insulation and regulation of humidity levels. The group has published a number of research papers on its findings.
High density pre-compressed bales (straw blocks) can bear higher loads than traditional field bales (bales created with baling machines on farms). While field bales support around of wall length, high-density bales can bear at least .
Bale buildings can also be constructed of non-straw bales—such as those made from recycled material such as tires, cardboard, paper, plastic, and carpeting—and even bags containing "bales" of wood chips or rice hulls.
Straw bales have also been used in very energy efficient high-performance buildings such as the S-House in Austria which meets the Passivhaus energy standard. In South Africa, a five-star lodge made from 10,000 strawbales has housed world leaders Nelson Mandela and Tony Blair. In the Swiss Alps, in the little village of Nax Mont-Noble, construction works have begun in October 2011 for the first hotel in Europe built entirely with straw bales. The Harrison Vault, in Joshua Tree, California, is engineered to withstand the high seismic loads in that area using only the assembly consisting of bales, lath and plaster. The technique was used successfully for strawbale housing in rural China. Straw bale domes along the Syrio-African rift at Kibbutz Lotan have an interior geodesic frame of steel pipes.
Another method to reap the benefits of straw is to incorporate straw-bale walls into a pre-existing structure.
Straw bales are widely used to insulate walls, but they may also be used to insulate roofs and sub-floors.
Thermal properties
Compressed straw bales have a wide range of documented R-value. R-value is a measurement of a materials insulating quality, higher the number the more insulating. The reported R-value ranges from 17–55 (in American units) or 3–9.6 (in SI) depending on the study, differing wall designs could be responsible for wide range in R-value. given that the bales are over a foot thick, the R-value per inch is lower than most other commercial insulation types including batts (3–4) and foamboard (~5). Bale walls are typically coated with a thick layer of plaster, which provides a well-distributed thermal mass, active on a short-term (diurnal) cycle. The combination of insulation and mass provide an excellent platform for passive solar building design for winter and summer.
In common with most building materials, there is a degree of uncertainty in the thermal conductivity due to the influences of temperature, moisture content and density. However, from evaluation of a range of literature and experimental data, a value of 0.064 W/m·K is regarded as a representative design value for straw bales at the densities typically used in building construction.
Compressed and plastered straw bale walls are also resistant to fire.
The hygrothermal properties of straw bales have been measured and reviewed in several technical papers. According to research, the thermal conductivity does not differ significantly depending on the type of straw. Samples with densities between 63 and 350 kg/m3 have been analysed. The best performing was characterised by a thermal conductivity of 0.038 W m−1 K−1. Marques et al., Reif et al. and Cascone et al. indicate that the thermal conductivity of straw is relatively insensitive to bale density. The thermal conductivity of straw bales has been shown to differ with the direction of the straw's orientation within the bale, with straws with fibres oriented perpendicularly or randomly to the heat flow having lower thermal conductivity than those arranged in parallel. For different temperatures and densities, Vjelien studied four variations of the same kind of straw: two variations concerned the direction of the fibres in relation to the heat flow: perpendicular and parallel, and the other two concerned the macrostructure chopped straw and defibrated straw. The thermal conductivity of the defibrated straw was lower than that of the chopped straw.
Efficiency
The use of straw bales as thermal insulation in buildings has been studied by many authors. They mainly focus on the straw’s thermal and hygrothermal properties. The findings showed that using straw in construction improves energy, environmental, and economic efficiency:
Some studies have evaluated the advantages of using straw bales for building insulation. Measurements carried out in an innovative and sustainable house built in France have shown that this material helps to minimize heating degrees and energy consumption. The simulated heating requirements in the winter are calculated to be 59 kW h/m2. In Italy, the energy-saving potential of a straw wall was assessed under various climatic conditions. As compared to the Italian regulations’ reference of a Net Zero Energy Building (NZEB), the straw wall performed extremely well in terms of energy efficiency. The embodied energy of a straw wall structure is about half that of a conventional wall assembly, and the corresponding CO2 emissions are more than 40% lower. Furthermore, in the summer, straw bale walls provide significant thermal inertia.
Liuzzi et al. compared expanded polystyrene (EPS), straw fibre, and olive fibre in a hygrothermal simulation of a flat in two different climatic zones (Bari and Bilbao), assuming a retrofit via interior panels. The simulation results show that the annual energy requirement when using straw fibre and olive fibre panels is close to the annual energy requirement for expanded polystyrene panels in both climates. During the cooling season, however, olive fibre and straw fibre insulation panels perform better, with a reduction of approximately 21% in Bilbao and 14% in Bari.
Straw has a thermal conductivity similar to that of common insulating materials. It has a thermal conductivity of 0.038–0.08 W m−1 K−1, which is comparable to other wood fibre insulation materials. To achieve the same thermal insulation efficiency as other more insulating materials such as extruded and extended polystyrene, the thickness of the straw insulation layer should be increased by 30–90%.
Problems with straw-bale
Two significant problems related to straw-bale construction are moisture and mold. During the construction phase, buildings need to be protected from rain and from water leakages into the body of the walls. If exposed to water, compressed straw may expand due to absorption of moisture. In turn, this can cause more cracking through which more moisture can infiltrate. Further damage to the wall can be caused by mold releasing potentially toxic spores into the wall cavities and into the air. In hot climates, where walls may have become internally dampened, internal temperatures may rise (due to decomposition of affected straw). Rats and mice can infiltrate straw bale homes during construction, so care must be taken to keep such animals out of the material. Other problems relate to straw dust which may cause breathing difficulties among people with allergies to straw or hay.
Several companies have developed prefabricated straw bale walls. A passive ecological house can easily be assembled with those panels.
See also
Truth window
Wintergreen Studios
References
Further reading
External links
Community Rebuilds - Nonprofit providing internships in straw bale construction and utilizing straw bale in affordable housing.
A History of the Straw Bale Resurgence at The Last Straw - a journal about straw bale building and other alternative forms of construction.
Rawlinson, Linnie. Artist Gordon Smedt's straw-bale house , feature on CNN.com, 13 August 2007. With image gallery.
Long Branch Environmental Education Center: Possible concerns regarding mold and humidity, technical paper, 2002.
"The Church That's Built Of Straw." Popular Mechanics, April 1960, pp. 130–131.
Straw Bale Housing in Rural China
History of Straw Bale Building and Straw Bale Building in Australia
Sustainable building
Construction
Sustainable technologies
Recycled building materials
Building | Straw-bale construction | [
"Engineering"
] | 2,930 | [
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341,407 | https://en.wikipedia.org/wiki/Damk%C3%B6hler%20numbers | The Damköhler numbers (Da) are dimensionless numbers used in chemical engineering to relate the chemical reaction timescale (reaction rate) to the transport phenomena rate occurring in a system. It is named after German chemist Gerhard Damköhler, who worked in chemical engineering, thermodynamics, and fluid dynamics.
The Karlovitz number (Ka) is related to the Damköhler number by Da = 1/Ka.
In its most commonly used form, the first Damköhler number (DaI) relates particles' characteristic residence time scale in a fluid region to the reaction timescale. The residence time scale can take the form of a convection time scale, such as volumetric flow rate through the reactor for continuous (plug flow or stirred tank) or semibatch chemical processes:
In reacting systems that include interphase mass transport, the first Damköhler number can be written as the ratio of the chemical reaction rate to the mass transfer rate
It is also defined as the ratio of the characteristic fluidic and chemical time scales:
Since the reaction rate determines the reaction timescale, the exact formula for the Damköhler number varies according to the rate law equation. For a general chemical reaction A → B following the Power law kinetics of n-th order, the Damköhler number for a convective flow system is defined as:
where:
k = kinetics reaction rate constant
C0 = initial concentration
n = reaction order
= mean residence time or space-time
On the other hand, the second Damköhler number (DaII) is defined in general as:
It compares the process energy of a thermochemical reaction (such as the energy involved in a nonequilibrium gas process) with a related enthalpy difference (driving force).
In terms of reaction rates:
where
kg is the global mass transport coefficient
a is the interfacial area
The value of Da provides a quick estimate of the degree of conversion that can be achieved. If DaI goes to infinity, the residence time greatly exceeds the reaction time, such that nearly all chemical reactions have taken place during the period of residency, this is the transport limited case, where the reaction is much faster than the diffusion. Otherwise if DaI goes to 0, the residence time is much shorter than the reaction time, so that no chemical reaction has taken place during the brief period when the fluid particles occupy the reaction location, this is the reaction limited case, where diffusion happens much faster than the reaction. Similarly, DaII goes to 0 implies that the energy of the chemical reaction is negligible compared to the energy of the flow. The limit of the Damköhler number going to infinity is called the Burke–Schumann limit.
As a rule of thumb, when Da is less than 0.1 a conversion of less than 10% is achieved, and when Da is greater than 10 a conversion of more than 90% is expected.
Derivation for decomposition of a single species
From the general mole balance on some species , where for a CSTR steady state and perfect mixing are assumed,
Assuming a constant volumetric flow rate , which is the case for a liquid reactor or a gas phase reaction with no net generation of moles,
where the space-time is defined to be the ratio of the reactor volume to volumetric flow rate. It is the time required for a slug of fluid to pass through the reactor. For a decomposition reaction, the rate of reaction is proportional to some power of the concentration of . In addition, for a single reaction a conversion may be defined in terms of the limiting reactant, for the simple decomposition that is species
As can be seen, as the Damköhler number increases, the other term must decrease. The ensuing polynomial can be solved and the conversion for the rule of thumb Damköhler numbers found. Alternatively, one can graph the expressions and see where they intersect with the line given by the inverse Damköhler number to see the solution for conversion. In the plot below, the y-axis is the inverse Damköhler number and the x-axis the conversion. The rule-of-thumb inverse Damköhler numbers have been placed as dashed horizontal lines.
References
Catalysis
Chemical reaction engineering
Dimensionless numbers of chemistry
Dimensionless numbers of fluid mechanics
Eponymous numbers in mathematics
Fluid dynamics | Damköhler numbers | [
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341,420 | https://en.wikipedia.org/wiki/Standard%20enthalpy%20of%20reaction | The standard enthalpy of reaction (denoted ) for a chemical reaction is the difference between total product and total reactant molar enthalpies, calculated for substances in their standard states. The value can be approximately interpreted in terms of the total of the chemical bond energies for bonds broken and bonds formed.
For a generic chemical reaction
the standard enthalpy of reaction is related to the standard enthalpy of formation values of the reactants and products by the following equation:
In this equation, are the stoichiometric coefficients of each product and reactant. The standard enthalpy of formation, which has been determined for a vast number of substances, is the change of enthalpy during the formation of 1 mole of the substance from its constituent elements, with all substances in their standard states.
Standard states can be defined at any temperature and pressure, so both the standard temperature and pressure must always be specified. Most values of standard thermochemical data are tabulated at either (25°C, 1 bar) or (25°C, 1 atm).
For ions in aqueous solution, the standard state is often chosen such that the aqueous H+ ion at a concentration of exactly 1 mole/liter has a standard enthalpy of formation equal to zero, which makes possible the tabulation of standard enthalpies for cations and anions at the same standard concentration. This convention is consistent with the use of the standard hydrogen electrode in the field of electrochemistry. However, there are other common choices in certain fields, including a standard concentration for H+ of exactly 1 mole/(kg solvent) (widely used in chemical engineering) and mole/L (used in the field of biochemistry).
Introduction
Two initial thermodynamic systems, each isolated in their separate states of internal thermodynamic equilibrium, can, by a thermodynamic operation, be coalesced into a single new final isolated thermodynamic system. If the initial systems differ in chemical constitution, then the eventual thermodynamic equilibrium of the final system can be the result of chemical reaction. Alternatively, an isolated thermodynamic system, in the absence of some catalyst, can be in a metastable equilibrium; introduction of a catalyst, or some other thermodynamic operation, such as release of a spark, can trigger a chemical reaction. The chemical reaction will, in general, transform some chemical potential energy into thermal energy. If the joint system is kept isolated, then its internal energy remains unchanged. Such thermal energy manifests itself, however, in changes in the non-chemical state variables (such as temperature, pressure, volume) of the joint systems, as well as the changes in the mole numbers of the chemical constituents that describe the chemical reaction.
Internal energy is defined with respect to some standard state. Subject to suitable thermodynamic operations, the chemical constituents of the final system can be brought to their respective standard states, along with transfer of energy as heat or through thermodynamic work, which can be measured or calculated from measurements of non-chemical state variables. Accordingly, the calculation of standard enthalpy of reaction is the most established way of quantifying the conversion of chemical potential energy into thermal energy.
Enthalpy of reaction for standard conditions defined and measured
The standard enthalpy of a reaction is defined so as to depend simply upon the standard conditions that are specified for it, not simply on the conditions under which the reactions actually occur. There are two general conditions under which thermochemical measurements are actually made.
(a) Constant volume and temperature: heat , where (sometimes written as ) is the internal energy of the system
(b) Constant pressure and temperature: heat , where is the enthalpy of the system
The magnitudes of the heat effects in these two conditions are different. In the first case the volume of the system is kept constant during the course of the measurement by carrying out the reaction in a closed and rigid container, and as there is no change in the volume no work is involved. From the first law of thermodynamics, , where W is the work done by the system. When only expansion work is possible for a process we have ; this implies that the heat of reaction at constant volume is equal to the change in the internal energy of the reacting system.
The thermal change that occurs in a chemical reaction is only due to the difference between the sum of internal energy of the products and the sum of the internal energy of reactants. We have
This also signifies that the amount of heat absorbed at constant volume could be identified with the change in the thermodynamic quantity internal energy.
At constant pressure on the other hand, the system is either kept open to the atmosphere or confined within a container on which a constant external pressure is exerted and under these conditions the volume of the system changes.
The thermal change at a constant pressure not only involves the change in the internal energy of the system but also the work performed either in expansion or contraction of the system. In general the first law requires that
(work)
If is only pressure–volume work, then at constant pressure
Assuming that the change in state variables is due solely to a chemical reaction, we have
As enthalpy or heat content is defined by , we have
By convention, the enthalpy of each element in its standard state is assigned a value of zero. If pure preparations of compounds or ions are not possible, then special further conventions are defined. Regardless, if each reactant and product can be prepared in its respective standard state, then the contribution of each species is equal to its molar enthalpy of formation multiplied by its stoichiometric coefficient in the reaction, and the enthalpy of reaction at constant (standard) pressure and constant temperature (usually 298 K) may be written as
As shown above, at constant pressure the heat of the reaction is exactly equal to the enthalpy change, , of the reacting system.
Variation with temperature or pressure
The variation of the enthalpy of reaction with temperature is given by Kirchhoff's Law of Thermochemistry, which states that the temperature derivative of ΔH for a chemical reaction is given by the difference in heat capacity (at constant pressure) between products and reactants:
.
Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.
Pressure variation effects and corrections due to mixing are generally minimal unless a reaction involves non-ideal gases and/or solutes, or is carried out at extremely high pressures. The enthalpy of mixing for a solution of ideal gases is exactly zero; the same is true for a reaction where the reactants and products are pure, unmixed components. Contributions to reaction enthalpies due to concentration variations for solutes in solution generally must be experimentally determined on a case by case basis, but would be exactly zero for ideal solutions since no change in the solution's average intermolecular forces as a function of concentration is possible in an ideal solution.
Subcategories
In each case the word standard implies that all reactants and products are in their standard states.
Standard enthalpy of combustion is the enthalpy change when one mole of an organic compound reacts with molecular oxygen (O2) to form carbon dioxide and liquid water. For example, the standard enthalpy of combustion of ethane gas refers to the reaction C2H6 (g) + (7/2) O2 (g) → 2 CO2 (g) + 3 H2O (l).
Standard enthalpy of formation is the enthalpy change when one mole of any compound is formed from its constituent elements in their standard states. The enthalpy of formation of one mole of ethane gas refers to the reaction 2 C (graphite) + 3 H2 (g) → C2H6 (g).
Standard enthalpy of hydrogenation is defined as the enthalpy change observed when one mole of an unsaturated compound reacts with an excess of hydrogen to become fully saturated. The hydrogenation of one mole of acetylene yields ethane as a product and is described by the equation C2H2 (g) + 2 H2 (g) → C2H6 (g).
Standard enthalpy of neutralization is the change in enthalpy that occurs when an acid and base undergo a neutralization reaction to form one mole of water. For example in aqueous solution, the standard enthalpy of neutralization of hydrochloric acid and the base magnesium hydroxide refers to the reaction HCl (aq) + 1/2 Mg(OH)2 → 1/2 MgCl2 (aq) + H2O(l).
Evaluation of reaction enthalpies
There are several methods of determining the values of reaction enthalpies, involving either measurements on the reaction of interest or calculations from data for related reactions.
For reactions which go rapidly to completion, it is often possible to measure the heat of reaction directly using a calorimeter. One large class of reactions for which such measurements are common is the combustion of organic compounds by reaction with molecular oxygen (O2) to form carbon dioxide and water (H2O). The heat of combustion can be measured with a so-called bomb calorimeter, in which the heat released by combustion at high temperature is lost to the surroundings as the system returns to its initial temperature. Since enthalpy is a state function, its value is the same for any path between given initial and final states, so that the measured ΔH is the same as if the temperature stayed constant during the combustion.
For reactions which are incomplete, the equilibrium constant can be determined as a function of temperature. The enthalpy of reaction is then found from the van 't Hoff equation as . A closely related technique is the use of an electroanalytical voltaic cell, which can be used to measure the Gibbs energy for certain reactions as a function of temperature, yielding and thereby .
It is also possible to evaluate the enthalpy of one reaction from the enthalpies of a number of other reactions whose sum is the reaction of interest, and these not need be formation reactions. This method is based on Hess's law, which states that the enthalpy change is the same for a chemical reaction which occurs as a single reaction or in several steps. If the enthalpies for each step can be measured, then their sum gives the enthalpy of the overall single reaction.
Finally the reaction enthalpy may be estimated using bond energies for the bonds which are broken and formed in the reaction of interest. This method is only approximate, however, because a reported bond energy is only an average value for different molecules with bonds between the same elements.
References
Enthalpy
Thermochemistry
Thermodynamics
pl:Standardowe molowe ciepło tworzenia | Standard enthalpy of reaction | [
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341,436 | https://en.wikipedia.org/wiki/State%20function | In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example. In this law, one state variable (e.g., pressure, volume, temperature, or the amount of substance in a gaseous equilibrium system) is a function of other state variables so is regarded as a state function. A state function could also describe the number of a certain type of atoms or molecules in a gaseous, liquid, or solid form in a heterogeneous or homogeneous mixture, or the amount of energy required to create such a system or change the system into a different equilibrium state.
Internal energy, enthalpy, and entropy are examples of state quantities or state functions because they quantitatively describe an equilibrium state of a thermodynamic system, regardless of how the system has arrived in that state. In contrast, mechanical work and heat are process quantities or path functions because their values depend on a specific "transition" (or "path") between two equilibrium states that a system has taken to reach the final equilibrium state. Exchanged heat (in certain discrete amounts) can be associated with changes of state function such as enthalpy. The description of the system heat exchange is done by a state function, and thus enthalpy changes point to an amount of heat. This can also apply to entropy when heat is compared to temperature. The description breaks down for quantities exhibiting hysteresis.
History
It is likely that the term "functions of state" was used in a loose sense during the 1850s and 1860s by those such as Rudolf Clausius, William Rankine, Peter Tait, and William Thomson. By the 1870s, the term had acquired a use of its own. In his 1873 paper "Graphical Methods in the Thermodynamics of Fluids", Willard Gibbs states: "The quantities v, p, t, ε, and η are determined when the state of the body is given, and it may be permitted to call them functions of the state of the body."
Overview
A thermodynamic system is described by a number of thermodynamic parameters (e.g. temperature, volume, or pressure) which are not necessarily independent. The number of parameters needed to describe the system is the dimension of the state space of the system (). For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system (). Any two-dimensional system is uniquely specified by two parameters. Choosing a different pair of parameters, such as pressure and volume instead of pressure and temperature, creates a different coordinate system in two-dimensional thermodynamic state space but is otherwise equivalent. Pressure and temperature can be used to find volume, pressure and volume can be used to find temperature, and temperature and volume can be used to find pressure. An analogous statement holds for higher-dimensional spaces, as described by the state postulate.
Generally, a state space is defined by an equation of the form , where denotes pressure, denotes temperature, denotes volume, and the ellipsis denotes other possible state variables like particle number and entropy . If the state space is two-dimensional as in the above example, it can be visualized as a three-dimensional graph (a surface in three-dimensional space). However, the labels of the axes are not unique (since there are more than three state variables in this case), and only two independent variables are necessary to define the state.
When a system changes state continuously, it traces out a "path" in the state space. The path can be specified by noting the values of the state parameters as the system traces out the path, whether as a function of time or a function of some other external variable. For example, having the pressure and volume as functions of time from time to will specify a path in two-dimensional state space. Any function of time can then be integrated over the path. For example, to calculate the work done by the system from time to time , calculate . In order to calculate the work in the above integral, the functions and must be known at each time over the entire path. In contrast, a state function only depends upon the system parameters' values at the endpoints of the path. For example, the following equation can be used to calculate the work plus the integral of over the path:
In the equation, can be expressed as the exact differential of the function . Therefore, the integral can be expressed as the difference in the value of at the end points of the integration. The product is therefore a state function of the system.
The notation will be used for an exact differential. In other words, the integral of will be equal to . The symbol will be reserved for an inexact differential, which cannot be integrated without full knowledge of the path. For example, will be used to denote an infinitesimal increment of work.
State functions represent quantities or properties of a thermodynamic system, while non-state functions represent a process during which the state functions change. For example, the state function is proportional to the internal energy of an ideal gas, but the work is the amount of energy transferred as the system performs work. Internal energy is identifiable; it is a particular form of energy. Work is the amount of energy that has changed its form or location.
List of state functions
The following are considered to be state functions in thermodynamics:
Mass
Energy ()
Enthalpy ()
Internal energy ()
Gibbs free energy ()
Helmholtz free energy ()
Exergy ()
Entropy ()
Pressure ()
Temperature ()
Volume ()
Chemical composition
Pressure altitude
Specific volume () or its reciprocal density ()
Particle number ()
See also
Markov property
Conservative vector field
Nonholonomic system
Equation of state
State variable
Notes
References
External links
Thermodynamic properties
Continuum mechanics | State function | [
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341,442 | https://en.wikipedia.org/wiki/Cantor%27s%20theorem | In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set , the set of all subsets of known as the power set of has a strictly greater cardinality than itself.
For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with elements has a total of subsets, and the theorem holds because for all non-negative integers.
Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also. As a consequence, the cardinality of the real numbers, which is the same as that of the power set of the integers, is strictly larger than the cardinality of the integers; see Cardinality of the continuum for details.
The theorem is named for Georg Cantor, who first stated and proved it at the end of the 19th century. Cantor's theorem had immediate and important consequences for the philosophy of mathematics. For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem, we obtain an endless hierarchy of infinite cardinals, each strictly larger than the one before it. Consequently, the theorem implies that there is no largest cardinal number (colloquially, "there's no largest infinity").
Proof
Cantor's argument is elegant and remarkably simple. The complete proof is presented below, with detailed explanations to follow.
By definition of cardinality, we have for any two sets and if and only if there is an injective function but no bijective function from It suffices to show that there is no surjection from . This is the heart of Cantor's theorem: there is no surjective function from any set to its power set. To establish this, it is enough to show that no function (that maps elements in to subsets of ) can reach every possible subset, i.e., we just need to demonstrate the existence of a subset of that is not equal to for any . Recalling that each is a subset of , such a subset is given by the following construction, sometimes called the Cantor diagonal set of :
This means, by definition, that for all , if and only if . For all the sets and cannot be equal because was constructed from elements of whose images under did not include themselves. For all either or . If then cannot equal because by assumption and by definition. If then cannot equal because by assumption and by the definition of .
Equivalently, and slightly more formally, we have just proved that the existence of such that implies the following contradiction:
Therefore, by reductio ad absurdum, the assumption must be false. Thus there is no such that ; in other words, is not in the image of and does not map onto every element of the power set of , i.e., is not surjective.
Finally, to complete the proof, we need to exhibit an injective function from to its power set. Finding such a function is trivial: just map to the singleton set . The argument is now complete, and we have established the strict inequality for any set that .
Another way to think of the proof is that , empty or non-empty, is always in the power set of . For to be onto, some element of must map to . But that leads to a contradiction: no element of can map to because that would contradict the criterion of membership in , thus the element mapping to must not be an element of meaning that it satisfies the criterion for membership in , another contradiction. So the assumption that an element of maps to must be false; and cannot be onto.
Because of the double occurrence of in the expression "", this is a diagonal argument. For a countable (or finite) set, the argument of the proof given above can be illustrated by constructing a table in which
each row is labelled by a unique from , in this order. is assumed to admit a linear order so that such table can be constructed.
each column of the table is labelled by a unique from the power set of ; the columns are ordered by the argument to , i.e. the column labels are , ..., in this order.
the intersection of each row and column records a true/false bit whether .
Given the order chosen for the row and column labels, the main diagonal of this table thus records whether for each . One such table will be the following:
The set constructed in the previous paragraphs coincides with the row labels for the subset of entries on this main diagonal (which in above example, coloured red) where the table records that is false. Each row records the values of the indicator function of the set corresponding to the column. The indicator function of coincides with the logically negated (swap "true" and "false") entries of the main diagonal. Thus the indicator function of does not agree with any column in at least one entry. Consequently, no column represents .
Despite the simplicity of the above proof, it is rather difficult for an automated theorem prover to produce it. The main difficulty lies in an automated discovery of the Cantor diagonal set. Lawrence Paulson noted in 1992 that Otter could not do it, whereas Isabelle could, albeit with a certain amount of direction in terms of tactics that might perhaps be considered cheating.
When A is countably infinite
Let us examine the proof for the specific case when is countably infinite. Without loss of generality, we may take , the set of natural numbers.
Suppose that is equinumerous with its power set . Let us see a sample of what looks like:
Indeed, contains infinite subsets of , e.g. the set of all positive even numbers , along with the empty set .
Now that we have an idea of what the elements of are, let us attempt to pair off each element of with each element of to show that these infinite sets are equinumerous. In other words, we will attempt to pair off each element of with an element from the infinite set , so that no element from either infinite set remains unpaired. Such an attempt to pair elements would look like this:
Given such a pairing, some natural numbers are paired with subsets that contain the very same number. For instance, in our example the number 2 is paired with the subset {1, 2, 3}, which contains 2 as a member. Let us call such numbers selfish. Other natural numbers are paired with subsets that do not contain them. For instance, in our example the number 1 is paired with the subset {4, 5}, which does not contain the number 1. Call these numbers non-selfish. Likewise, 3 and 4 are non-selfish.
Using this idea, let us build a special set of natural numbers. This set will provide the contradiction we seek. Let be the set of all non-selfish natural numbers. By definition, the power set contains all sets of natural numbers, and so it contains this set as an element. If the mapping is bijective, must be paired off with some natural number, say . However, this causes a problem. If is in , then is selfish because it is in the corresponding set, which contradicts the definition of . If is not in , then it is non-selfish and it should instead be a member of . Therefore, no such element which maps to can exist.
Since there is no natural number which can be paired with , we have contradicted our original supposition, that there is a bijection between and .
Note that the set may be empty. This would mean that every natural number maps to a subset of natural numbers that contains . Then, every number maps to a nonempty set and no number maps to the empty set. But the empty set is a member of , so the mapping still does not cover .
Through this proof by contradiction we have proven that the cardinality of and cannot be equal. We also know that the cardinality of cannot be less than the cardinality of because contains all singletons, by definition, and these singletons form a "copy" of inside of . Therefore, only one possibility remains, and that is that the cardinality of is strictly greater than the cardinality of , proving Cantor's theorem.
Related paradoxes
Cantor's theorem and its proof are closely related to two paradoxes of set theory.
Cantor's paradox is the name given to a contradiction following from Cantor's theorem together with the assumption that there is a set containing all sets, the universal set . In order to distinguish this paradox from the next one discussed below, it is important to note what this contradiction is. By Cantor's theorem for any set . On the other hand, all elements of are sets, and thus contained in , therefore .
Another paradox can be derived from the proof of Cantor's theorem by instantiating the function f with the identity function; this turns Cantor's diagonal set into what is sometimes called the Russell set of a given set A:
The proof of Cantor's theorem is straightforwardly adapted to show that assuming a set of all sets U exists, then considering its Russell set RU leads to the contradiction:
This argument is known as Russell's paradox. As a point of subtlety, the version of Russell's paradox we have presented here is actually a theorem of Zermelo; we can conclude from the contradiction obtained that we must reject the hypothesis that RU∈U, thus disproving the existence of a set containing all sets. This was possible because we have used restricted comprehension (as featured in ZFC) in the definition of RA above, which in turn entailed that
Had we used unrestricted comprehension (as in Frege's system for instance) by defining the Russell set simply as , then the axiom system itself would have entailed the contradiction, with no further hypotheses needed.
Despite the syntactical similarities between the Russell set (in either variant) and the Cantor diagonal set, Alonzo Church emphasized that Russell's paradox is independent of considerations of cardinality and its underlying notions like one-to-one correspondence.
History
Cantor gave essentially this proof in a paper published in 1891 "Über eine elementare Frage der Mannigfaltigkeitslehre", where the diagonal argument for the uncountability of the reals also first appears (he had earlier proved the uncountability of the reals by other methods). The version of this argument he gave in that paper was phrased in terms of indicator functions on a set rather than subsets of a set. He showed that if f is a function defined on X whose values are 2-valued functions on X, then the 2-valued function G(x) = 1 − f(x)(x) is not in the range of f.
Bertrand Russell has a very similar proof in Principles of Mathematics (1903, section 348), where he shows that there are more propositional functions than objects. "For suppose a correlation of all objects and some propositional functions to have been affected, and let phi-x be the correlate of x. Then "not-phi-x(x)," i.e. "phi-x does not hold of x" is a propositional function not contained in this correlation; for it is true or false of x according as phi-x is false or true of x, and therefore it differs from phi-x for every value of x." He attributes the idea behind the proof to Cantor.
Ernst Zermelo has a theorem (which he calls "Cantor's Theorem") that is identical to the form above in the paper that became the foundation of modern set theory ("Untersuchungen über die Grundlagen der Mengenlehre I"), published in 1908. See Zermelo set theory.
Generalizations
Lawvere's fixed-point theorem provides for a broad generalization of Cantor's theorem to any category with finite products in the following way: let be such a category, and let be a terminal object in . Suppose that is an object in and that there exists an endomorphism that does not have any fixed points; that is, there is no morphism that satisfies . Then there is no object of such that a morphism can parameterize all morphisms . In other words, for every object and every morphism , an attempt to write maps as maps of the form must leave out at least one map .
See also
Schröder–Bernstein theorem
Cantor's first uncountability proof
Controversy over Cantor's theory
References
Halmos, Paul, Naive Set Theory. Princeton, NJ: D. Van Nostrand Company, 1960. Reprinted by Springer-Verlag, New York, 1974. (Springer-Verlag edition). Reprinted by Martino Fine Books, 2011. (Paperback edition).
External links
1891 introductions
1891 in science
Set theory
Theorems in the foundations of mathematics
Cardinal numbers
Georg Cantor | Cantor's theorem | [
"Mathematics"
] | 2,669 | [
"Cardinal numbers",
"Foundations of mathematics",
"Set theory",
"Mathematical logic",
"Mathematical objects",
"Infinity",
"Numbers",
"Mathematical problems",
"Mathematical theorems",
"Theorems in the foundations of mathematics"
] |
341,482 | https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem%20theorem | In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem.
The precise formulation is given below. It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism.
As a consequence, first-order theories are unable to control the cardinality of their infinite models.
The (downward) Löwenheim–Skolem theorem is one of the two key properties, along with the compactness theorem, that are used in Lindström's theorem to characterize first-order logic.
In general, the Löwenheim–Skolem theorem does not hold in stronger logics such as second-order logic.
Theorem
In its general form, the Löwenheim–Skolem Theorem states that for every signature σ, every infinite σ-structure M and every infinite cardinal number , there is a σ-structure N such that and such that
if then N is an elementary substructure of M;
if then N is an elementary extension of M.
The theorem is often divided into two parts corresponding to the two cases above. The part of the theorem asserting that a structure has elementary substructures of all smaller infinite cardinalities is known as the downward Löwenheim–Skolem Theorem. The part of the theorem asserting that a structure has elementary extensions of all larger cardinalities is known as the upward Löwenheim–Skolem Theorem.
Discussion
Below we elaborate on the general concept of signatures and structures.
Concepts
Signatures
A signature consists of a set of function symbols Sfunc, a set of relation symbols Srel, and a function representing the arity of function and relation symbols. (A nullary function symbol is called a constant symbol.) In the context of first-order logic, a signature is sometimes called a language. It is called countable if the set of function and relation symbols in it is countable, and in general the cardinality of a signature is the cardinality of the set of all the symbols it contains.
A first-order theory consists of a fixed signature and a fixed set of sentences (formulas with no free variables) in that signature. Theories are often specified by giving a list of axioms that generate the theory, or by giving a structure and taking the theory to consist of the sentences satisfied by the structure.
Structures / Models
Given a signature σ, a σ-structure M
is a concrete interpretation of the symbols in σ. It consists of an underlying set (often also denoted by "M") together with an interpretation of the function and relation symbols of σ. An interpretation of a constant symbol of σ in M is simply an element of M. More generally, an interpretation of an n-ary function symbol f is a function from Mn to M. Similarly, an interpretation of a relation symbol R is an n-ary relation on M, i.e. a subset of Mn.
A substructure of a σ-structure M is obtained by taking a subset N of M which is closed under the interpretations of all the function symbols in σ (hence includes the interpretations of all constant symbols in σ), and then restricting the interpretations of the relation symbols to N. An elementary substructure is a very special case of this; in particular an elementary substructure satisfies exactly the same first-order sentences as the original structure (its elementary extension).
Consequences
The statement given in the introduction follows immediately by taking M to be an infinite model of the theory. The proof of the upward part of the theorem also shows that a theory with arbitrarily large finite models must have an infinite model; sometimes this is considered to be part of the theorem.
A theory is called categorical if it has only one model, up to isomorphism. This term was introduced by , and for some time thereafter mathematicians hoped they could put mathematics on a solid foundation by describing a categorical first-order theory of some version of set theory. The Löwenheim–Skolem theorem dealt a first blow to this hope, as it implies that a first-order theory which has an infinite model cannot be categorical. Later, in 1931, the hope was shattered completely by Gödel's incompleteness theorem.
Many consequences of the Löwenheim–Skolem theorem seemed counterintuitive to logicians in the early 20th century, as the distinction between first-order and non-first-order properties was not yet understood. One such consequence is the existence of uncountable models of true arithmetic, which satisfy every first-order induction axiom but have non-inductive subsets.
Let N denote the natural numbers and R the reals. It follows from the theorem that the theory of (N, +, ×, 0, 1) (the theory of true first-order arithmetic) has uncountable models, and that the theory of (R, +, ×, 0, 1) (the theory of real closed fields) has a countable model. There are, of course, axiomatizations characterizing (N, +, ×, 0, 1) and (R, +, ×, 0, 1) up to isomorphism.
The Löwenheim–Skolem theorem shows that these axiomatizations cannot be first-order.
For example, in the theory of the real numbers, the completeness of a linear order used to characterize R as a complete ordered field, is a non-first-order property.
Another consequence that was considered particularly troubling is the existence of a countable model of set theory, which nevertheless must satisfy the sentence saying the real numbers are uncountable. Cantor's theorem states that some sets are uncountable. This counterintuitive situation came to be known as Skolem's paradox; it shows that the notion of countability is not absolute.
Proof sketch
Downward part
For each first-order -formula , the axiom of choice implies the existence of a function
such that, for all , either
or
.
Applying the axiom of choice again we get a function from the first-order formulas to such functions .
The family of functions gives rise to a preclosure operator on the power set of
for .
Iterating countably many times results in a closure operator . Taking an arbitrary subset such that , and having defined , one can see that also . Then is an elementary substructure of by the Tarski–Vaught test.
The trick used in this proof is essentially due to Skolem, who introduced function symbols for the Skolem functions into the language. One could also define the as partial functions such that is defined if and only if . The only important point is that is a preclosure operator such that contains a solution for every formula with parameters in which has a solution in and that
.
Upward part
First, one extends the signature by adding a new constant symbol for every element of . The complete theory of for the extended signature is called the elementary diagram of . In the next step one adds many new constant symbols to the signature and adds to the elementary diagram of the sentences for any two distinct new constant symbols and . Using the compactness theorem, the resulting theory is easily seen to be consistent. Since its models must have cardinality at least , the downward part of this theorem guarantees the existence of a model which has cardinality exactly . It contains an isomorphic copy of as an elementary substructure.
In other logics
Although the (classical) Löwenheim–Skolem theorem is tied very closely to first-order logic, variants hold for other logics. For example, every consistent theory in second-order logic has a model smaller than the first supercompact cardinal (assuming one exists). The minimum size at which a (downward) Löwenheim–Skolem–type theorem applies in a logic is known as the Löwenheim number, and can be used to characterize that logic's strength. Moreover, if we go beyond first-order logic, we must give up one of three things: countable compactness, the downward Löwenheim–Skolem Theorem, or the properties of an abstract logic.
Historical notes
This account is based mainly on . To understand the early history of model theory one must distinguish between syntactical consistency (no contradiction can be derived using the deduction rules for first-order logic) and satisfiability (there is a model). Somewhat surprisingly, even before the completeness theorem made the distinction unnecessary, the term consistent was used sometimes in one sense and sometimes in the other.
The first significant result in what later became model theory was Löwenheim's theorem in Leopold Löwenheim's publication "Über Möglichkeiten im Relativkalkül" (1915):
For every countable signature σ, every σ-sentence that is satisfiable is satisfiable in a countable model.
Löwenheim's paper was actually concerned with the more general Peirce–Schröder calculus of relatives (relation algebra with quantifiers). He also used the now antiquated notations of Ernst Schröder. For a summary of the paper in English and using modern notations see .
According to the received historical view, Löwenheim's proof was faulty because it implicitly used Kőnig's lemma without proving it, although the lemma was not yet a published result at the time. In a revisionist account, considers that Löwenheim's proof was complete.
gave a (correct) proof using formulas in what would later be called Skolem normal form and relying on the axiom of choice:
Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M.
also proved the following weaker version without the axiom of choice:
Every countable theory which is satisfiable in a model is also satisfiable in a countable model.
simplified . Finally, Anatoly Ivanovich Maltsev (Анато́лий Ива́нович Ма́льцев, 1936) proved the Löwenheim–Skolem theorem in its full generality . He cited a note by Skolem, according to which the theorem had been proved by Alfred Tarski in a seminar in 1928. Therefore, the general theorem is sometimes known as the Löwenheim–Skolem–Tarski theorem. But Tarski did not remember his proof, and it remains a mystery how he could do it without the compactness theorem.
It is somewhat ironic that Skolem's name is connected with the upward direction of the theorem as well as with the downward direction:
"I follow custom in calling Corollary 6.1.4 the upward Löwenheim-Skolem theorem. But in fact Skolem didn't even believe it, because he didn't believe in the existence of uncountable sets." – .
"Skolem [...] rejected the result as meaningless; Tarski [...] very reasonably responded that Skolem's formalist viewpoint ought to reckon the downward Löwenheim-Skolem theorem meaningless just like the upward." – .
"Legend has it that Thoralf Skolem, up until the end of his life, was scandalized by the association of his name to a result of this type, which he considered an absurdity, nondenumerable sets being, for him, fictions without real existence." – .
References
Sources
The Löwenheim–Skolem theorem is treated in all introductory texts on model theory or mathematical logic.
Historical publications
()
()
()
Secondary sources
; A more concise account appears in chapter 9 of
External links
Burris, Stanley N., Contributions of the Logicians, Part II, From Richard Dedekind to Gerhard Gentzen
Burris, Stanley N., Downward Löwenheim–Skolem theorem
Simpson, Stephen G. (1998), Model Theory
Mathematical logic
Metatheorems
Model theory
Theorems in the foundations of mathematics | Löwenheim–Skolem theorem | [
"Mathematics"
] | 2,547 | [
"Foundations of mathematics",
"Mathematical logic",
"Model theory",
"Mathematical problems",
"Mathematical theorems",
"Theorems in the foundations of mathematics"
] |
341,566 | https://en.wikipedia.org/wiki/Halite | Halite ( ), commonly known as rock salt, is a type of salt, the mineral (natural) form of sodium chloride (NaCl). Halite forms isometric crystals. The mineral is typically colorless or white, but may also be light blue, dark blue, purple, pink, red, orange, yellow or gray depending on inclusion of other materials, impurities, and structural or isotopic abnormalities in the crystals. It commonly occurs with other evaporite deposit minerals such as several of the sulfates, halides, and borates. The name halite is derived from the Ancient Greek word for "salt", ἅλς (háls).
Occurrence
Halite dominantly occurs within sedimentary rocks where it has formed from the evaporation of seawater or salty lake water. Vast beds of sedimentary evaporite minerals, including halite, can result from the drying up of enclosed lakes and restricted seas. Such salt beds may be hundreds of meters thick and underlie broad areas. Halite occurs at the surface today in playas in regions where evaporation exceeds precipitation such as in the salt flats of Badwater Basin in Death Valley National Park.
In the United States and Canada, extensive underground beds extend from the Appalachian Basin of western New York through parts of Ontario and under much of the Michigan Basin. Other deposits are in Ohio, Kansas, New Mexico, Nova Scotia and Saskatchewan. Deposits can also be found near Dasol, Pangasinan, Philippines. The Khewra salt mine is a massive deposit of halite near Islamabad, Pakistan.
Salt domes are vertical diapirs or pipe-like masses of salt that have been essentially "squeezed up" from underlying salt beds by mobilization due to the weight of the overlying rock. Salt domes contain anhydrite, gypsum, and native sulfur, in addition to halite and sylvite. They are common along the Gulf coasts of Texas and Louisiana and are often associated with petroleum deposits. Germany, Spain, the Netherlands, Denmark, Romania and Iran also have salt domes. Salt glaciers exist in arid Iran where the salt has broken through the surface at high elevation and flows downhill. In these cases, halite is said to be behaving like a rheid.
Unusual, purple, fibrous vein-filling halite is found in France and a few other localities. Halite crystals termed hopper crystals appear to be "skeletons" of the typical cubes, with the edges present and stairstep depressions on, or rather in, each crystal face. In a rapidly crystallizing environment, the edges of the cubes simply grow faster than the centers. Halite crystals form very quickly in some rapidly evaporating lakes resulting in modern artifacts with a coating or encrustation of halite crystals. Halite flowers are rare stalactites of curling fibers of halite that are found in certain arid caves of Australia's Nullarbor Plain. Halite stalactites and encrustations are also reported in the Quincy native copper mine of Hancock, Michigan.
Mining
The world's largest underground salt mine is the Sifto Salt Mine. It produces over 7 million tons of rock salt per year using the room and pillar mining method. It is located half a kilometre under Lake Huron in Ontario, Canada. In the United Kingdom there are three mines; the largest of these is at Winsford in Cheshire, producing, on average, one million tonnes of salt per year.
Uses
Salt is used extensively in cooking as a flavor enhancer, and to cure a wide variety of foods such as bacon and fish. It is frequently used in food preservation methods across various cultures. Larger pieces can be ground in a salt mill or dusted over food from a shaker as finishing salt.
Halite is also often used both residentially and municipally for managing ice. Because brine (a solution of water and salt) has a lower freezing point than pure water, putting salt or saltwater on ice that is below will cause it to melt—this effect is called freezing-point depression. It is common for homeowners in cold climates to spread salt on their sidewalks and driveways after a snow storm to melt the ice. It is not necessary to use so much salt that the ice is completely melted; rather, a small amount of salt will weaken the ice so that it can be easily removed by other means. Also, many cities will spread a mixture of sand and salt on roads during and after a snowstorm to improve traction. Using salt brine is more effective than spreading dry salt because moisture is necessary for the freezing-point depression to work and wet salt sticks to the roads better. Otherwise the salt can be wiped away by traffic.
In addition to de-icing, rock salt is occasionally used in agriculture. An example of this would be inducing salt stress to suppress the growth of annual meadow grass in turf production. Other examples involve exposing weeds to salt water to dehydrate and kill them preventing them from affecting other plants. Salt is also used as a household cleaning product. Its coarse nature allows for its use in various cleaning scenarios including grease/oil removal, stain removal, dries out and hardens sticky spills for an easier clean.
Some cultures, especially in Africa and Brazil, prefer a wide variety of different rock salts for different dishes. Pure salt is avoided as particular colors of salt indicates the presence of different impurities. Many recipes call for particular kinds of rock salt, and imported pure salt often has impurities added to adapt to local tastes. Historically, salt was used as a form of currency in barter systems and was exclusively controlled by authorities and their appointees. In some ancient civilizations the practice of salting the earth was done to make conquered land of an enemy infertile and inhospitable as an act of domination or spite. One biblical reference to this practice is in Judges 9:45: "he killed the people in it, pulled the wall down and sowed the site with salt."
Polyhalite, a mineral fertilizer, is not an NaCl-polymer, but hydrated sulfate of potassium, calcium and magnesium (K2Ca2Mg-sulfate).
Shotgun shells containing rock salt (instead of metal pellets) are a less lethal deterrent.
Gallery
See also
Coarse salt (edible)
Salt tectonics
Grozon coal and saltworks
References
External links
Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., John Wiley and Sons, New York
Anthony, John W; Bideaux, R.A.; Bladh, K.W.; Nicois, M.C. (1997). Handbook of Mineralogy: Halides, Hydroxides, Oxides, Mineral Data Publishing, Tucson
Minerals.net
Material Safety Data Sheet
Desert USA
Halite stalactites
Sodium minerals
Chloride minerals
Cubic minerals
Minerals in space group 225
Edible salt
Evaporite
Luminescent minerals
Industrial minerals
Rocksalt group | Halite | [
"Chemistry"
] | 1,434 | [
"Edible salt",
"Luminescence",
"Luminescent minerals",
"Salts"
] |
599,837 | https://en.wikipedia.org/wiki/Habituation | Habituation is a form of non-associative learning in which an organism’s non-reinforced response to a stimulus decreases after repeated or prolonged presentations of that stimulus. For example, organisms may habituate to repeated sudden loud noises when they learn that these have no consequences.
Habituation can occur in responses that habituate include those that involve an entire organism or specific biological component systems of an organism. The broad ubiquity of habituation across all forms of life has led to it being called "the simplest, most universal form of learning...as fundamental a characteristic of life as DNA." Functionally, habituation is thought to free up cognitive resources for other stimuli that are associated with biologically important events by diminishing the response to inconsequential stimuli.
A progressive decline of a behavior in a habituation procedure may also reflect nonspecific effects such as fatigue, which must be ruled out when the interest is in habituation. Habituation is relevant in psychiatry and psychopathology, as several neuropsychiatric conditions including autism, schizophrenia, migraine, and Tourette syndrome show reduced habituation to a variety of stimulus-types both simple and complex.
Drug habituation
There is an additional connotation to the term habituation which applies to psychological dependency on drugs, and is included in several online dictionaries. A team of specialists from the World Health Organization assembled in 1957 to address the problem of drug addiction and adopted the term "drug habituation" to distinguish some drug-use behaviors from drug addiction. According to the WHO lexicon of alcohol and drug terms, habituation is defined as "becoming accustomed to any behavior or condition, including psychoactive substance use". By 1964, the report of the Surgeon General of the United States on smoking and health included four features that characterize drug habituation according to WHO: 1) "a desire (but not a compulsion) to continue taking the drug for the sense of improved well-being which it engenders"; 2) "little or no tendency to increase the dose"; 3) "some degree of psychic dependence on the effect of the drug, but absence of physical dependence and hence of an abstinence syndrome"; 4) "detrimental effects, if any, primarily on the individual". However, also in 1964, a committee from the World Health Organization once again convened and decided the definitions of drug habituation and drug addiction were insufficient, replacing the two terms with "drug dependence". Substance dependence is the preferred term today when describing drug-related disorders, whereas the use of the term drug habituation has declined substantially. This is not to be confused with true habituation to drugs, wherein repeated doses have an increasingly diminished effect, as is often seen in addicts or persons taking painkillers frequently.
Characteristics
Habituation as a form of non-associative learning can be distinguished from other behavioral changes (e.g., sensory/neural adaptation, fatigue) by considering the characteristics of habituation that have been identified over several decades of research. The characteristics first described by Thompson and Spencer were updated in 2008 and 2009, to include the following:
Repeated presentation of a stimulus will cause a decrease in reaction to the stimulus. Habituation is also proclaimed to be a form of implicit learning, which is commonly the case with continually repeated stimuli. This characteristic is consistent with the definition of habituation as a procedure, but to confirm habituation as a process, additional characteristics must be demonstrated. Also observed is spontaneous recovery. That is, a habituated response to a stimulus recovers (increases in magnitude) when a significant amount of time (hours, days, weeks) passes between stimulus presentations.
"Potentiation of habituation" is observed when tests of spontaneous recovery are given repeatedly. In this phenomenon, the decrease in responding that follows spontaneous recovery becomes more rapid with each test of spontaneous recovery. Also noted was that an increase in the frequency of stimulus presentation (i.e., shorter interstimulus interval) will increase the rate of habituation. Furthermore, continued exposure to the stimulus after the habituated response has plateaued (i.e., show no further decrement) may have additional effects on subsequent tests of behavior such as delaying spontaneous recovery. The concepts of stimulus generalization and stimulus discrimination will be observed. Habituation to an original stimulus will also occur to other stimuli that are similar to the original stimulus (stimulus generalization). The more similar the new stimulus is to the original stimulus, the greater the habituation that will be observed. When a subject shows habituation to a new stimulus that is similar to the original stimulus but not to a stimulus that is different from the original stimulus, then the subject is showing stimulus discrimination. (For example, if one was habituated to the taste of lemon, their responding would increase significantly when presented with the taste of lime). Stimulus discrimination can be used to rule out sensory adaptation and fatigue as an alternative explanation of the habituation process.
Another observation mentioned is when a single introduction of a different stimulus late in the habituation procedure when responding to the eliciting stimulus has declined can cause an increase in the habituated response. This increase in responding is temporary and is called "dishabituation" and always occurs to the original eliciting stimulus (not to the added stimulus). Researchers also use evidence of dishabituation to rule out sensory adaptation and fatigue as alternative explanations of the habituation process. Habituation of dishabituation can occur. The amount of dishabituation that occurs as a result of the introduction of a different stimulus can decrease after repeated presentation of the "dishabituating" stimulus.
Some habituation procedures appear to result in a habituation process that last days or weeks. This is considered long-term habituation. It persists over long durations of time (i.e., shows little or no spontaneous recovery). Long-term habituation can be distinguished from short-term habituation which is identified by the nine characteristics listed above.
Biological mechanisms
The changes in synaptic transmission that occur during habituation have been well-characterized in the Aplysia gill and siphon withdrawal reflex. Habituation has been shown in essentially every species of animal and at least, in one species of plants (Mimosa pudica), in isolated neuronally-differentiated cell-lines, as well as in quantum perovskite. The experimental investigation of simple organisms such as the large protozoan Stentor coeruleus provides an understanding of the cellular mechanisms that are involved in the habituation process.
Neuroimaging
Within psychology, habituation has been studied through different forms of neuroimaging like PET scan and fMRI. Within fMRI, the response that habituates is the blood oxygen level-dependent (BOLD) signals triggered by stimuli. Decreases of the BOLD signal are interpreted as habituation.
The amygdala is one of the most-studied areas of the brain in relation to habituation. A common approach is to observe the visual processing of facial expressions. A study by Breiter and colleagues used fMRI scans to identify which areas of the brain habituate and at what rate. Their results showed that the human amygdala responds and rapidly habituates preferentially to fearful facial expressions over neutral ones. They also observed significant amygdala signal changes in response to happy faces over neutral faces.
Blackford, Allen, Cowan, and Avery (2012) compared the effect of an extremely inhibited temperament and an extremely uninhibited temperament on habituation. Their study found that over repeated presentations individuals with an uninhibited temperament demonstrated habituation in both the amygdala and hippocampus, whereas participants with an inhibited temperament demonstrated habituation in neither brain region. The researchers suggest that this failure to habituate reflects a social learning deficit in individuals with an extremely inhibited temperament, which is a possible mechanism for a higher risk of social anxiety.
Debate about learning-status
Although habituation has been regarded as a learning process by some as early as 1887, its learning status remained controversial up until the 1920s - 1930s. While conceding that reflexes may "relax" or otherwise decrease with repeated stimulation, the "invariance doctrine" stipulated that reflexes should not remain constant and that variable reflexes were a pathological manifestation. Indeed, air pilots who showed habituation of post-rotational nystagmus reflex were sometimes ejected from or not recruited for service for World War I: on the grounds that a variable reflex response indicated either a defective vestibular apparatus or a lack of vigilance. Eventually, however, more research from the medical and scientific communities concluded that stimulus-dependent variability reflexes is clinically normal. The opposition to the considering habituation a form of learning was also based on the assumption that learning processes must produce novel behavioral responses and must occur in the cerebral cortex. Non-associative forms of learning such as habituation (and sensitization) do not produce novel (conditioned) responses but rather diminish a pre-existing (innate) responses and often are shown to depend on peripheral (non-cerebral) synaptic changes in the sensory-motor pathway. Most modern learning theorists, however, consider any behavioral change that occurs as a result of experience to be learning, so long as it cannot be accounted for by motor fatigue, sensory adaptation, developmental changes or damage.
Criteria for verifying a response-decline as learning
Importantly, systematic response-declines can be produced by non-learning factors such as sensory adaptation (obstruction of stimulus detection), motor fatigue, or damage. Three diagnostic criteria are used to distinguish response-declines produced by these non-learning factors and response-declines produced by habituation (learning) processes. These are:
Recovery by Dishabituation
Sensitivity of Spontaneous Recovery to Rate-of-Stimulation
Stimulus-specificity
Early studies relied on the demonstration of 1) Recovery by Dishabituation (the brief recovery of the response to the eliciting stimulus when another stimulus is added) to distinguish habituation from sensory adaptation and fatigue. More recently, 2) Sensitivity of Spontaneous Recovery to Rate-of-Stimulation and 3) Stimulus-specificity have been used as experimental evidence for the habituation process. Spontaneous Recovery is sensitive to spontaneous recovery, showing recovery that is inversely correlated with the amount of response-decline. This is the opposite of what would be expected if sensory adaptation or motor fatigue were the cause of the response-decline. Sensory adaptation (or neural adaptation) occurs when an organism can no longer detect the stimulus as efficiently as when first presented and motor fatigue occurs when an organism is able to detect the stimulus but can no longer respond efficiently. Stimulus-specificity stipulates that the response-decline is not general (due to motor fatigue) but occurs only to the original stimulus that was repeated. If a response-decline shows 1) dishabituation, 2) spontaneous recovery that is inversely correlated with the extent of decline, and/or 3) stimulus-specificity, then habituation learning is supported.
Despite the ubiquity of habituation and its modern acceptance as a genuine form of learning it has not enjoyed the same focus within research as other forms of learning. On this topic, the animal psychologist James McConnell said "...nobody cares…much about habituation"). It has been suggested that the apathy held towards habituation is due to 1) resistance from traditional learning theorists maintain memory requires reproduction of propositional/linguistic content; 2) resistance from behaviorists who maintain that "true" learning requires the development of a novel response (whereas habituation is a decrease in a pre-existing response); 3) the behavioral measure of habituation (i.e., a response-decline) is very susceptible to confound by non-learning factors (e.g., fatigue) which, therefore, make it more difficult to study).
Theories
Various models have been proposed to account for habituation including the Stimulus-Model Comparator theory formulated by Evgeny Sokolov, the Groves and Thompson dual-process theory, and the SOP (Standard Operating Procedures/Sometimes Opponent Process) model formulated by Allan Wagner
Stimulus-model comparator theory
The stimulus-model comparator theory emerged from the research of Sokolov who used the orienting response as the cornerstone of his studies, and operationally defining the orienting response as EEG activity. Orienting responses are heightened sensitivity experienced by an organism when exposed to a new or changing stimulus. Orienting responses can result in overt, observable behaviors as well as psychophysiological responses such as EEG activity and undergo habituation with repeated presentation of the eliciting stimulus. The Sokolov model assumes that when a stimulus is experienced several times, the nervous system creates a model of the expected stimulus (a stimulus model). With additional presentations of the stimulus, the experienced stimulus is compared with the stimulus model. If the experienced stimulus matches the stimulus model, responding is inhibited. At first the stimulus model is not a very good representation of the presented stimulus, and thus responding continues because of this mismatch. With additional presentations the stimulus model is improved, there is no longer a mismatch, and responding is inhibited causing habituation. However, if the stimulus is changed so that it no longer matches the stimulus model, the orienting response is no longer inhibited. Sokolov locates the stimulus model in the cerebral cortex.
Dual-process theory
The Groves and Thompson dual-process theory of habituation posits that two separate processes exist in the central nervous system that interacts to produce habituation. The two distinct processes are a habituation process and a sensitization process. The dual-process theory argues that all noticeable stimuli will elicit both of these processes and that the behavioral output will reflect a summation of both processes. The habituation process is decremental, whereas the sensitization process is incremental enhancing the tendency to respond. Thus when the habituation process exceeds the sensitization process behavior shows habituation, but if the sensitization process exceeds the habituation process, behavior shows sensitization. Groves and Thompson hypothesize the existence of two neural pathways: an "S-R pathway" involved with the habituation process, and a "state pathway" involved with sensitization. The state system is seen as equivalent to a general state of arousal.
Examples of the habituation process in animals and humans
Habituation has been observed in an enormously wide range of species from motile single-celled organisms such as the amoeba and Stentor coeruleus to sea slugs to humans. Habituation processes are adaptive, allowing animals to adjust their innate behaviors to changes in their natural world. A natural animal instinct, for example, is to protect themselves and their territory from any danger and potential predators. An animal needs to respond quickly to the sudden appearance of a predator. What may be less obvious is the importance of defensive responses to the sudden appearance of any new, unfamiliar stimulus, whether it is dangerous or not. An initial defensive response to a new stimulus is important because if an animal fails to respond to a potentially dangerous unknown stimulus, the results could be deadly. Despite this initial, innate defensive response to an unfamiliar stimulus, the response becomes habituated if the stimulus repeatedly occurs but causes no harm. An example of this is the prairie dog habituating to humans. Prairie dogs give alarm calls when they detect a potentially dangerous stimulus. This defensive call occurs when any mammal, snake, or large bird approaches them. However, they habituate to noises, such as human footsteps, that occur repeatedly but result in no harm to them. If prairie dogs never habituate to nonthreatening stimuli, they would be constantly sending out alarm calls and wasting their time and energy. However, the habituation process in prairie dogs may depend on several factors including the particular defensive response. In one study that measured several different responses to the repeated presence of humans, the alarm calls of prairie dogs showed habituation whereas the behavior of escaping into their burrows showed sensitization.
Another example of the importance of habituation in the animal world is provided by a study with harbor seals. In one study researchers measured the responses of harbor seals to underwater calls of different types of killer whales. The seals showed a strong response when they heard the calls of mammal-eating killer whales. However, they did not respond strongly when hearing familiar calls of the local fish-eating population. The seals, therefore, are capable of habituating to the calls of harmless predators, in this case, harmless killer whales. While some researchers prefer to simply describe the adaptive value of observable habituated behavior, others find it useful to infer psychological processes from the observed behavior change. For example, habituation of aggressive responses in male bullfrogs has been explained as "an attentional or learning process that allows animals to form enduring mental representations of the physical properties of a repeated stimulus and to shift their focus of attention away from sources of irrelevant or unimportant stimulation".
Habituation of innate defensive behaviors is also adaptive in humans, such as habituation of a startle response to a sudden loud noise. But habituation is much more ubiquitous even in humans. An example of habituation that is an essential element of everyone's life is the changing response to food as it is repeatedly experienced during a meal. When people eat the same food during a meal, they begin to respond less to the food as they become habituated to the motivating properties of the food and decrease their consumption. Eating less during a meal is usually interpreted as reaching satiety or "getting full", but experiments suggest that habituation also plays an important role. Many experiments with animals and humans have shown that providing variety in a meal increases the amount that is consumed in a meal, most likely because habituation is stimulus-specific and because variety may introduce dishabituation effects. Food variety also slows the rate of habituation in children and may be an important contributing factor to the recent increases in obesity.
Richard Solomon and John Corbit (1974) proposed the opponent-process theory, arguing that habituation is also found in emotional responses. This theory proposes that not all emotional reactions to a stimulus change in the same way when the stimulus is presented repeatedly: some weaken (decrease) while others are strengthened (increase). The overall effect is that an outside stimulus provokes an emotional reaction that increases rapidly until it is at its most intense. Gradually, the emotional state declines to a level lower than normal and eventually returns to neutral. This pattern coincides with two internal processes referred to as the a-process and b-process. Hence, the opponent-process theory predicts that subjects will show no reaction following a stimulus after a repetition of this same stimulus. It is the after-reaction that is much larger and prolonged than if an initial reaction to a stimulus occurred.
Relevance to neuropsychiatry
Habituation abnormalities have been repeatedly observed in a variety of neuropsychiatric conditions including autism spectrum disorder (ASD), fragile X syndrome, schizophrenia, Parkinson's disease (PD), Huntington's disease (HD), attention deficit hyperactivity disorder (ADHD), Tourette's syndrome (TS), and migraine. In human clinical studies, habituation is most often studied using the acoustic startle reflex; acoustic tones are delivered to participants through headphones and the subsequent eye-blink response is recorded directly by observation or by electromyography (EMG). Depending on the disorder, habituation phenomena have been implicated as a cause, symptom, or therapy. Reduced habituation is the most common habituation phenotype reported across neuropsychiatric disorders although enhanced habituation has been observed in HD and ADHD. It also appears that abnormal habituation is often predictive of symptom severity in several neuropsychiatric disorders, including ASD, PD, and HD. Moreover, there are instances where treatments that normalise the habituation-deficit also improve other associated symptoms. As a therapy, habituation processes have been hypothesized to underlie the efficacy of behavioural therapies (i.e. habit reversal training, exposure therapy) for TS and PTSD, although extinction processes may be operating instead.
Uses and challenges of the habituation procedure
Habituation procedures are used by researchers for many reasons. For example, in a study on aggression in female chimpanzees from a group known as the "Kasakela Chimpanzee Community", researchers habituated the chimpanzees by repeatedly exposing them to the presence of human beings. Their efforts to habituate the chimpanzees before the field researchers studied the animal's behavior was necessary in order for them to eventually be able to note the natural behavior of the chimpanzees, instead of simply noting chimpanzee behavior as a response to the presence of the researchers. In another study, Mitumba chimpanzees in the Gombe National Park were habituated for at least four years before the introduction of systematic data collection.
Researchers also use habituation and dishabituation procedures in the laboratory to study the perceptual and cognitive capabilities of human infants. The presentation of a visual stimulus to an infant elicits looking behavior that habituates with repeated presentations of the stimulus. When changes to the habituated stimulus are made (or a new stimulus is introduced), the looking behavior returns (dishabituates). A recent fMRI study revealed that the presentation of a dishabituating stimulus has an observable, physical effect upon the brain. In one study the mental spatial representations of infants were assessed using the phenomenon of dishabituation. Infants were presented repeatedly with an object in the same position on a table. Once the infants habituated to the object (i.e., spent less time looking at it) either the object was spatially moved while the infant remained at the same place near the table or the object was left in the same place but the infant was moved to the opposite side of the table. In both cases, the spatial relationship between the object and the infant had changed, but only in the former case did the object itself move. Would the infants know the difference? Or would they treat both cases as if the object itself moved? The results revealed a return of looking behavior (dishabituation) when the object's position was changed, but not when the infant's position was changed. Dishabituation indicates that infants perceived a significant change in the stimulus. Therefore, the infants understood when the object itself moved and when it did not. Only when the object itself moved were they interested in it again (dishabituation). When the object remained in the same position as before it was perceived as the same old boring thing (habituation). In general, habituation/dishabituation procedures help researchers determine the way infants perceive their environments.
Habituation is a useful primary tool for then assessing mental processes in the stages of infancy. The purpose for these tests, or paradigms records looking time, which is the baseline measurement. Habituation of looking time helps to assess certain child capabilities such as: memory, sensitivity, and helps the baby recognize certain abstract properties. Habituation is also found to be influenced by unchangeable factors such as infant age, gender, and complexity of the stimulus. (Caron & Caron, 1969; Cohen, DeLoache, & Rissman, 1975; Friedman, Nagy, & Carpenter, 1970; Miller, 1972; Wetherford & Cohen, 1973).
Though there are various challenges that come with habituation. Some infants have preferences for some stimuli based on their static or dynamic properties. Infant dishabituation also is not perceived as a direct measure for mental processes as well. In previous theories of habituation, an infant's dishabituation was thought to represent their own realization of the remembered stimulus of stimuli. For example: if infants would be dishabituated to a certain color item to a new item, it would be noticed that they remembered the color and compared the two colors for differences. Also, another challenge that comes with habituation is the dichotomy of novelty vs familiar stimuli. If an infant preferred a novel still, this meant the infant observed the new spatial relation of the object, but not the object itself. If an infant preferred familiarity, the infant would notice the pattern of the stimuli, instead of the actual new stimuli.
The habituation/dishabituation procedure is also used to discover the resolution of perceptual systems. For instance, by habituating someone to one stimulus, and then observing responses to similar ones, one can detect the smallest degree of difference that is detectable.
See also
Adaptive system
Aplysia
Consumer demand tests (animals)
Contact hypothesis
Desensitization (psychology)
Hedonic adaptation
Konrad Lorenz, Behind the Mirror: A Search for a Natural History of Human Knowledge: on habituation
Preference tests (animals)
Tachyphylaxis, the effect of continued exogenous entries (habituation of) into the metabolism of an organism within the scope/field of biological chemistry
References
Further reading
External links
Dana Sugu & Amita Chaterjee 'Flashback: Reshuffling Emotions', International Journal on Humanistic Ideology, Vol. 3 No. 1, Spring-Summer 2010
Usabilityfirst.com.=913 "Definition of Habituation". Retrieved August 29, 2008.
BBC "Definition in context". Retrieved August 24, 2009.
Behavioral concepts
Learning | Habituation | [
"Biology"
] | 5,271 | [
"Behavior",
"Behavioral concepts",
"Behaviorism"
] |
599,870 | https://en.wikipedia.org/wiki/Observer%20bias | Observer bias is one of the types of detection bias and is defined as any kind of systematic divergence from accurate facts during observation and the recording of data and information in studies. The definition can be further expanded upon to include the systematic difference between what is observed due to variation in observers, and what the true value is.
Observer bias is the tendency of observers to not see what is there, but instead to see what they expect or want to see. This is a common occurrence in the everyday lives of many and is a significant problem that is sometimes encountered in scientific research and studies. Observation is critical to scientific research and activity, and as such, observer bias may be as well. When such biases exist, scientific studies can result in an over- or underestimation of what is true and accurate, which compromises the validity of the findings and results of the study, even if all other designs and procedures in the study were appropriate.
Observational data forms the foundation of a significant body of knowledge. Observation is a method of data collection and falls into the category of qualitative research techniques. There are a number of benefits of observation, including its simplicity as a data collection method and its usefulness for hypotheses. Simultaneously, there are many limitations and disadvantages in the observation process, including the potential lack of reliability, poor validity, and faulty perception. Participants' observations are widely used in sociological and anthropological studies, while systematic observation is used where researchers need to collect data without participants direct interactions. The most common observation method is naturalistic observation, where subjects are observed in their natural environments with the goal to assess the behaviour in an intervention free and natural setting.
Observer bias is especially probable when the investigator or researcher has vested interests in the outcome of the research or has strong preconceptions. Coupled with ambiguous underlying data and a subjective scoring method, these three factors contribute heavily to the incidence of observer bias.
Examples
Examples of observer bias extend back to the early 1900's. One of the first recorded events of apparent observer bias was seen in 1904, with the case of "Clever Hans". Clever Hans was a horse whose owner, Wilhem von Olson, claimed could solve arithmetic equations. Von Olson would ask Clever Hans a series of questions involving arithmetic functions, and the horse would appear to answer by tapping its hoof with the numbered answer. This example was investigated by the psychologist Oskar Pfungst, and it was found that when the horse was nearing the correct number of taps, the owner would subconsciously react in a particular way, which signalled to Clever Hans to discontinue his tapping. This only worked, however, when the owner himself knew the answer to the question. This is an example of observer bias, due to the fact that the expectations of von Olson, the horse's owner, were the cause of Clever Hans actions and behaviours, resulting in faulty data.
One of the most notorious examples of observer bias is seen in the studies and contributions of Cyril Burt, an English psychologist and geneticist who purported the heritability of IQ. Burt believed, and thus demonstrated through his research because of his observer bias, that children from families with lower socioeconomic status were likely to have lower levels of cognitive abilities when compared with that of children from families with higher socioeconomic status. Such research and findings had considerable impacts on the educational system in England throughout the 1960s, where middle- and upper-class children were sent to elite schools while the children from the lower socioeconomic demographic were sent to schools with less desirable traits. Following Burt's death, further research found that the data in Burt's studies was fabricated, which was presumed to be a result of his observer bias and the outcomes he was intending to find through his studies.
Another key example of observer bias is a 1963 study, "Psychology of the Scientist: V. Three Experiments in Experimenter Bias", published by researchers Robert Rosenthal and Kermit L. Fode at the University of North Dakota. In this study, Rosenthal and Fode gave a group of twelve psychology students a total of sixty rats to run in some experiments. The students were told that they either had "maze-bright" rats, who were bred to be exceptionally good at solving mazes, or that they had "maze-dull" rats, who were bred to be poor at solving mazes. They were then asked to run experiments with the rats and collect the data as they usually would. The rats were placed in T-shaped mazes where they had to run down the center and then decide to turn left or turn right. One of the sides of the maze was painted white, while the other was painted dark gray, and it was the rat's job to always turn towards the dark gray side of the maze. The rats who turned towards the dark gray side of the maze received a reward, while the rats who turned towards the white side of the maze did not. The students kept track of how many times each rat turned towards the correct (or dark gray) side of the maze, how many times each rat turned towards the incorrect (or white) side of the maze, and how long it took each rat to make a decision. They repeated this experiment ten times per day, all over the course of five days total, and in the end, they found that the "maze-bright" rats were better at both correctly completing the maze and completing the maze in the fastest time. However, there were actually no "maze-bright" or "maze-dull" rats; these rats were all genetically identical to one another and were randomly divided into the two categories. The two groups of students should have gotten the same results for both kinds of rats, but failed to do so because of observer bias. The entire effect of the experiment was caused by their expectations: they expected that the "maze-bright" rats would perform better and that the "maze-dull" rats would perform worse. Rosenthal and Fode concluded that these results were caused by smaller and more subtle biases on the part of the students. The students were unaware of the fact that they were treating the rats differently. It's possible that they had slightly different criteria for when the two groups of rats finished the maze, that they had the tendency to hit the stopwatch later for the "maze-dull" rats, or that they were paying more attention to the "maze-bright" rats overall. In this way, the students, or the observers, created what looked like a real result, but what was, in reality, totally false.
Impact
Observational data forms the foundation of a significant body of knowledge. Observer bias can be seen as a significant issue in medical research and treatment. There is greater potential for variance in observations made where subjective judgement is required, when compared with observation of objective data where there is a much lower risk of observer bias.
When there is observer bias present in research and studies, the data collection itself is affected. The findings and results are not accurate representations of reality, due to the influence of the observers' biases. Although they may not intend to do so, observer bias may result in researchers subconsciously encouraging certain results, which would lead to changes in the findings and outcomes in the study. A researcher that has not taken steps to mitigate observer bias and is being influenced by their own observer bias has a higher probability of making erroneous interpretations, which ultimately will lead to inaccurate results and findings.
Research has shown that in the presence of observer bias in outcome assessment, it is possible for treatment effect estimates to be exaggerated by between a third to two-thirds, symbolising significant implications on the validity of the findings and results of studies and procedures.
Preventative steps
Bias is unfortunately an unavoidable problem in epidemiological and clinical research. However, there are a number of potential strategies and solutions for the reduction of observer bias, specifically in the areas of scientific studies and research across the medical field. The effects that bias has can be reduced through the use of strong operational definitions, along with masking, triangulation, and standardisation of procedures, and the continual monitoring of the objectivity of those conducting the experiments and observations. In market research surveys, researchers have described a framework called bias testing to mitigate researcher bias by empirically testing the survey questions with real-life respondents, and to not lead the respondents, neutral probing and redirecting techniques are used.
Blinded protocols and double-blinded research can act as a corrective lens in terms of reducing observer bias, and thus, to increase the reliability and accuracy of the data collected. Blind trials are often required in order for the attainment of regulatory approval for medical devices and drugs, but are not common practice in empirical studies despite the research supporting its necessity. Double-blinding is done by ensuring both the tester and research participants lack of information that could have a potential influence on their behaviour, while single-blind describes those experiments where information is withheld from the participants that may otherwise skew the results or introduce bias, but the experimenter is entirely aware of and in possession of those facts.
An example of how observer bias can impact on research, and how blinded protocols can impact, can be seen in the trial for an anti-psychotic drug. Researchers that know which of the subjects received the placebo and those that received the trial drugs may later report that the group that received the trial drugs had a calmer disposition, due to the expectations of that outcome. Similarly, if the participants in the trial were not blinded, then they may report how they are feeling differently based on whether they were provided with the placebo or the trial drug.
A further example could be seen at schools. Boys of school-age generally outperform their female peers in science, however there is evidence that this is potentially as a result of how they are taught and treated by their teachers, who have the expectation that the boys have higher performances, and thus subtly encourage them. As such, the observers, being the teachers who conduct tests and evaluate the results, have a bias and preconceived belief that boys will outperform girls, which impacts on their behaviour.
To complement blind or masked protocols and research, further strategies including standardised training for observers and researchers about how to record findings can be useful in the mitigation of observer bias. Clear definition of methodology, tools and the time frames allocated for the collection of findings can assist in adequately training and preparing observers in a standardised manner. Further, identifying any potential conflicts of interest within observers before commencement of the research is essential in ensuring bias is minimised.
Finally, triangulation within research is a method that can be used to increase the findings validity and credibility. Triangulation in research refers to the use of a variety of methods or data sources as a means of developing a more comprehensive and accurate understanding of the subject at hand. Triangulation will considerably increase the confidence in a study tremendously. There are a few ways triangulation can occur, including the use of multiple observers, which is a form of reliability in itself called interobserver reliability, measured by the percentage of times that the observers agree.
Hawthorne effect (observer effect)
Observer bias is commonly only identified in the observers, however, there also exists a bias for those being studied. Named after a series of experiments conducted by Elton Mayo between 1924 and 1932, at the Western Electric factory in Hawthorne, Chicago, the Hawthorne effect symbolises where the participants in a study change their behaviour due to the fact that they are being observed.
Within the Hawthorne studies, it was found that the departmental outputs increased each time a change was made, even when the changes made were reverting to the original unfavourable conditions. The subjects in the experiment were told that better lighting would result in improved productivity, and as such, their beliefs about the impact of good lighting had a more significant effect on their behaviour and output than what the actual lighting levels were. Researchers formed the conclusion that the workers were in fact responding to the attention of the supervisors, not the changes in the experimental variables.
To prevent the Hawthorne effect, studies using hidden observation can be useful. However, knowledge of participation in the study would be required by law and is thought to still have the potential to cause the induction of the Hawthorne effect. Further, making responses or study data completely anonymous will result in reducing the likelihood of participants altering their behaviour as a result of being observed as they take part in an experiment or study. Furthermore, conducting research prior to the studies to establish a baseline measure could assist in mitigating the Hawthorne effect from biasing the studies results significantly. With a baseline established, any potential participant bias that arises as a result of being observed can be evaluated. Furthermore, establishing a follow-up period could be of benefit to enable the examination of whether a behaviour or change continues and is sustained beyond the observation period.
See also
Observer-expectancy effect, when a researcher subconsciously influences the participants of an experiment
References
Experimental bias | Observer bias | [
"Mathematics"
] | 2,638 | [
"Experimental bias",
"Statistical concepts"
] |
599,966 | https://en.wikipedia.org/wiki/New%20Calendarists | The New Calendarists are Eastern Orthodox churches that adopted the Revised Julian calendar.
Background
In the history of Christianity, divisions on which calendar to use were initiated after 1582, when the Catholic Church transitioned from the ancient Julian calendar to the new Gregorian calendar.
Eventually, by the 18th century, the Gregorian Calendar was officially adopted even in Protestant countries as the civil calendar, but still faced some opposition from smaller groups. In the Kingdom of Great Britain, the Gregorian calendar was officially introduced in 1752.
Around the same time, debates between those wanting to adopt the Gregorian Calendar and traditionalists wanting to keep the Julian calendar were also going on within several Eastern Catholic Churches. Those debates were focused mainly on ritual questions and ended in various compromises. The need for preservation of ritual differences, including various questions related to liturgical calendar, was consequently acknowledged by Rome.
New Calendarists
In 1923, the Revised Julian calendar was devised. Since then, several Eastern Orthodox Churches have introduced partial changes into their liturgical calendars. Those changes were based on the application of the Revised Julian calendar for the liturgical celebration of immovable feasts (including Christmas), thus reducing the use of the old Julian calendar to liturgical celebration of moveable feasts (feasts of the Easter cycle).
Thus, the Revised calendar use was introduced. It has been adopted by:
the Ecumenical Patriarchate (March 1924)
the Church of Greece (March 1924)
the Church of Cyprus (March 1924)
the Romanian Orthodox Church (later in 1924)
the Patriarchate of Alexandria (in 1928)
the Patriarchate of Antioch (in 1928)
the Albanian Orthodox Church (April 1937)
the Bulgarian Orthodox Church (in 1968)
the Orthodox Church of Ukraine (in 2023)
The Orthodox Church in America (except for Alaska) also uses the revised calendar.
It was not adopted by the Eastern Orthodox Churches of:
Jerusalem
Georgia
Russia
Sinai
the monasteries on the Mount Athos.
The Polish Orthodox Church has wavered between the two calendars; today it officially follows the old calendar.
In Eastern Orthodoxy, issues related to calendar reform did not produce break of communion or schisms between the mainstream churches, but they did cause disputes and internal schisms within some churches. The result of those conflicts was the emergence of the Old Calendarist movement, and consequent creation of separate churches, thus breaking the communion with those mother churches that accepted the calendar reform.
See also
Adoption of the Gregorian calendar
French revolutionary calendar
Revised Julian calendar
Old Calendarists
References
Sources
Calendars
History of Eastern Christianity
History of Eastern Orthodoxy
Liturgical calendars
Old Calendarism
Julian calendar | New Calendarists | [
"Physics"
] | 515 | [
"Spacetime",
"Calendars",
"Physical quantities",
"Time"
] |
599,970 | https://en.wikipedia.org/wiki/List%20of%20lemmas | This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.
Algebra
Abhyankar's lemma
Aubin–Lions lemma
Bergman's diamond lemma
Fitting lemma
Injective test lemma
Hua's lemma (exponential sums)
Krull's separation lemma
Schanuel's lemma (projective modules)
Schwartz–Zippel lemma
Shapiro's lemma
Stewart–Walker lemma (tensors)
Whitehead's lemma (Lie algebras)
Zariski's lemma
Algebraic geometry
Abhyankar's lemma
Fundamental lemma (Langlands program)
Category theory
Five lemma
Horseshoe lemma
Nine lemma
Short five lemma
Snake lemma
Splitting lemma
Yoneda lemma
Linear algebra
Matrix determinant lemma
Matrix inversion lemma
Group theory
Burnside's lemma also known as the Cauchy–Frobenius lemma
Frattini's lemma (finite groups)
Goursat's lemma
Mautner's lemma (representation theory)
Ping-pong lemma (geometric group theory)
Schreier's subgroup lemma
Schur's lemma (representation theory)
Zassenhaus lemma
Polynomials
Gauss's lemma (polynomials)
Schwartz–Zippel lemma
Ring theory and commutative algebra
Artin–Rees lemma
Hensel's lemma (commutative rings)
Nakayama lemma
Noether's normalization lemma
Prime avoidance lemma
Universal algebra
Jónsson's lemma
Analysis
Fekete's lemma
Fundamental lemma of calculus of variations
Hopf lemma
Sard's lemma (singularity theory)
Stechkin's lemma (functional and numerical analysis)
Vitali covering lemma (real analysis)
Watson's lemma
Complex analysis
Estimation lemma (contour integrals)
Hartogs's lemma (several complex variables)
Jordan's lemma
Lemma on the Logarithmic derivative
Schwarz lemma
Fourier analysis
Riemann–Lebesgue lemma
Differential equations
Borel's lemma (partial differential equations)
Grönwall's lemma
Lax–Milgram lemma
Pugh's closing lemma
Weyl's lemma (Laplace equation) (partial differential equations)
Differential forms
Poincaré lemma of closed and exact differential forms
Functional analysis
Cotlar–Stein lemma
Ehrling's lemma
Riesz's lemma
Mathematical series
Abel's lemma
Kronecker's lemma
Numerical analysis
Bramble–Hilbert lemma
Céa's lemma
Applied mathematics
Danielson–Lanczos lemma (Fourier transforms)
Farkas's lemma (linear programming)
Feld–Tai lemma (electromagnetism)
Little's lemma (queuing theory)
Finsler's lemma
Control theory
Finsler's lemma
Hautus lemma
Kalman–Yakubovich–Popov lemma
Computational complexity theory
Isolation lemma
Switching lemma
Cryptography
Forking lemma
Leftover hash lemma
Piling-up lemma (linear cryptanalysis)
Yao's XOR lemma
Formal languages
Interchange lemma
Newman's lemma (term rewriting)
Ogden's lemma
Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
Hotelling's lemma
Shephard's lemma
Combinatorics
Cousin's lemma (integrals)
Dickson's lemma
Littlewood–Offord lemma
Pólya–Burnside lemma
Sperner's lemma
Ky Fan lemma (combinatorial geometry)
Graph theory
Berge's lemma
Counting lemma
Crossing lemma
Expander mixing lemma
Handshaking lemma
Kelly's lemma
Kőnig's lemma
Szemerédi regularity lemma
Order theory
Higman's lemma
Ultrafilter lemma
Dynamical systems
Barbalat's lemma
Kac's lemma (ergodic theory)
Geometry
Shadowing lemma
Big-little-big lemma (mathematics of paper folding)
Gordan's lemma
Hilbert's lemma
Euclidean geometry
Archimedes's lemmas
Johnson–Lindenstrauss lemma (Euclidean geometry)
Hyperbolic geometry
Margulis lemma
Metric spaces
Lebesgue's number lemma (dimension theory)
Riemannian geometry
Gauss's lemma (Riemannian geometry)
Mathematical logic
Craig interpolation lemma
Diagonal lemma
Lindenbaum's lemma
Mostowski collapse lemma
Teichmüller–Tukey lemma also known as Tukey's lemma
Zorn's lemma; equivalent to the axiom of choice
Set theory
Covering lemma
Delta lemma
Dynkin lemma
Fodor's lemma
Fixed-point lemma for normal functions (axiomatic set theory)
Moschovakis coding lemma
Rasiowa–Sikorski lemma
Number theory
Bézout's lemma
Dwork's lemma
Euclid's lemma
Gauss's lemma
Hensel's lemma
Zolotarev's lemma
Siegel's lemma (Diophantine approximation)
Analytic number theory
Hua's lemma
Vaughan's lemma
Diophantine equations
Bhaskara's lemma
Sieve theory
Fundamental lemma of sieve theory
Probability theory
Borel–Cantelli lemma
Doob–Dynkin lemma
Itô's lemma (stochastic calculus)
Lovász local lemma
Stein's lemma
Wald's lemma
Statistics
Glivenko–Cantelli lemma
Neyman–Pearson lemma
Robbins lemma
Measure theory
Factorization lemma
Fatou's lemma
Frostman's lemma (geometric measure theory)
Malliavin's absolute continuity lemma
Topology
Lindelöf's lemma
Urysohn's lemma
Tube lemma
Differential topology
Morse lemma
Fixed-point theory
Knaster–Kuratowski–Mazurkiewicz lemma
Geometric topology
Dehn's lemma
Topological groups and semigroups
Ellis–Numakura lemma (topological semigroups)
Lemmas | List of lemmas | [
"Mathematics"
] | 1,318 | [
"Mathematical theorems",
"Mathematical problems",
"Lemmas"
] |
600,011 | https://en.wikipedia.org/wiki/List%20of%20conjectures | This is a list of notable mathematical conjectures.
Open problems
The following conjectures remain open. The (incomplete) column "cites" lists the number of results for a Google Scholar search for the term, in double quotes .
Conjectures now proved (theorems)
The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic names.
Deligne's conjecture on 1-motives
Goldbach's weak conjecture (proved in 2013)
Sensitivity conjecture (proved in 2019)
Disproved (no longer conjectures)
The conjectures in following list were not necessarily generally accepted as true before being disproved.
Atiyah conjecture (not a conjecture to start with)
Borsuk's conjecture
Chinese hypothesis (not a conjecture to start with)
Doomsday conjecture
Euler's sum of powers conjecture
Ganea conjecture
Generalized Smith conjecture
Hauptvermutung
Hedetniemi's conjecture, counterexample announced 2019
Hirsch conjecture (disproved in 2010)
Intersection graph conjecture
Kelvin's conjecture
Kouchnirenko's conjecture
Mertens conjecture
Pólya conjecture, 1919 (1958)
Ragsdale conjecture
Schoenflies conjecture (disproved 1910)
Tait's conjecture
Von Neumann conjecture
Weyl–Berry conjecture
Williamson conjecture
In mathematics, ideas are supposedly not accepted as fact until they have been rigorously proved. However, there have been some ideas that were fairly accepted in the past but which were subsequently shown to be false. The following list is meant to serve as a repository for compiling a list of such ideas.
The idea of the Pythagoreans that all numbers can be expressed as a ratio of two whole numbers. This was disproved by one of Pythagoras' own disciples, Hippasus, who showed that the square root of two is what we today call an irrational number. One story claims that he was thrown off the ship in which he and some other Pythagoreans were sailing because his discovery was too heretical.
Euclid's parallel postulate stated that if two lines cross a third in a plane in such a way that the sum of the "interior angles" is not 180° then the two lines meet. Furthermore, he implicitly assumed that two separate intersecting lines meet at only one point. These assumptions were believed to be true for more than 2000 years, but in light of General Relativity at least the second can no longer be considered true. In fact the very notion of a straight line in four-dimensional curved space-time has to be redefined, which one can do as a geodesic. (But the notion of a plane does not carry over.) It is now recognized that Euclidean geometry can be studied as a mathematical abstraction, but that the universe is non-Euclidean.
Fermat conjectured that all numbers of the form (known as Fermat numbers) were prime. However, this conjecture was disproved by Euler, who found that
The idea that transcendental numbers were unusual. Disproved by Georg Cantor who showed that there are so many transcendental numbers that it is impossible to make a one-to-one mapping between them and the algebraic numbers. In other words, the cardinality of the set of transcendentals (denoted ) is greater than that of the set of algebraic numbers ().
Bernhard Riemann, at the end of his famous 1859 paper "On the Number of Primes Less Than a Given Magnitude", stated (based on his results) that the logarithmic integral gives a somewhat too high estimate of the prime-counting function. The evidence also seemed to indicate this. However, in 1914 J. E. Littlewood proved that this was not always the case, and in fact it is now known that the first x for which occurs somewhere before 10317. See Skewes' number for more detail.
Naïvely it might be expected that a continuous function must have a derivative or else that the set of points where it is not differentiable should be "small" in some sense. This was disproved in 1872 by Karl Weierstrass, and in fact examples had been found earlier of functions that were nowhere differentiable (see Weierstrass function). According to Weierstrass in his paper, earlier mathematicians including Gauss had often assumed that such functions did not exist.
It was conjectured in 1919 by George Pólya, based on the evidence, that most numbers less than any particular limit have an odd number of prime factors. However, this Pólya conjecture was disproved in 1958. It turns out that for some values of the limit (such as values a bit more than 906 million), most numbers less than the limit have an even number of prime factors.
Erik Christopher Zeeman tried for 7 years to prove that one cannot untie a knot on a 4-sphere. Then one day he decided to try to prove the opposite, and he succeeded in a few hours.
A "theorem" of Jan-Erik Roos in 1961 stated that in an [AB4*] abelian category, lim1 vanishes on Mittag-Leffler sequences. This "theorem" was used by many people since then, but it was disproved by counterexample in 2002 by Amnon Neeman.
See also
Erdős conjectures
Fuglede's conjecture
Millennium Prize Problems
Painlevé conjecture
Mathematical fallacy
Superseded theories in science
List of incomplete proofs
List of unsolved problems in mathematics
List of disproved mathematical ideas
List of unsolved problems
List of lemmas
List of theorems
List of statements undecidable in ZFC
References
Further reading
External links
Open Problem Garden
Conjectures|Disproved mathematical ideas | List of conjectures | [
"Mathematics"
] | 1,183 | [
"Unsolved problems in mathematics",
"Mathematical problems",
"Conjectures"
] |
600,030 | https://en.wikipedia.org/wiki/Poincar%C3%A9%20lemma | In mathematics, the Poincaré lemma gives a sufficient condition for a closed differential form to be exact (while an exact form is necessarily closed). Precisely, it states that every closed p-form on an open ball in Rn is exact for p with . The lemma was introduced by Henri Poincaré in 1886.
Especially in calculus, the Poincaré lemma also says that every closed 1-form on a simply connected open subset in is exact.
In the language of cohomology, the Poincaré lemma says that the k-th de Rham cohomology group of a contractible open subset of a manifold M (e.g., ) vanishes for . In particular, it implies that the de Rham complex yields a resolution of the constant sheaf on M. The singular cohomology of a contractible space vanishes in positive degree, but the Poincaré lemma does not follow from this, since the fact that the singular cohomology of a manifold can be computed as the de Rham cohomology of it, that is, the de Rham theorem, relies on the Poincaré lemma. It does, however, mean that it is enough to prove the Poincaré lemma for open balls; the version for contractible manifolds then follows from the topological consideration.
The Poincaré lemma is also a special case of the homotopy invariance of de Rham cohomology; in fact, it is common to establish the lemma by showing the homotopy invariance or at least a version of it.
Proofs
A standard proof of the Poincaré lemma uses the homotopy invariance formula (cf. see the proofs below as well as Integration along fibers#Example). The local form of the homotopy operator is described in and the connection of the lemma with the Maurer-Cartan form is explained in .
Direct proof
The Poincaré lemma can be proved by means of integration along fibers. (This approach is a straightforward generalization of constructing a primitive function by means of integration in calculus.)
We shall prove the lemma for an open subset that is star-shaped or a cone over ; i.e., if is in , then is in for . This case in particular covers the open ball case, since an open ball can be assumed to centered at the origin without loss of generality.
The trick is to consider differential forms on (we use for the coordinate on ). First define the operator (called the fiber integration) for k-forms on by
where , and similarly for and . Now, for , since , using the differentiation under the integral sign, we have:
where denote the restrictions of to the hyperplanes and they are zero since is zero there. If , then a similar computation gives
.
Thus, the above formula holds for any -form on . Finally, let and then set . Then, with the notation , we get: for any -form on ,
the formula known as the homotopy formula. The operator is called the homotopy operator (also called a chain homotopy). Now, if is closed, . On the other hand, and , the latter because there is no nonzero higher form at a point. Hence,
which proves the Poincaré lemma.
The same proof in fact shows the Poincaré lemma for any contractible open subset U of a manifold. Indeed, given such a U, we have the homotopy with the identity and a point. Approximating such ,, we can assume is in fact smooth. The fiber integration is also defined for . Hence, the same argument goes through.
Proof using Lie derivatives
Cartan's magic formula for Lie derivatives can be used to give a short proof of the Poincaré lemma. The formula states that the Lie derivative along a vector field is given as:
where denotes the interior product; i.e., .
Let be a smooth family of smooth maps for some open subset U of such that is defined for t in some closed interval I and is a diffeomorphism for t in the interior of I. Let denote the tangent vectors to the curve ; i.e., . For a fixed t in the interior of I, let . Then . Thus, by the definition of a Lie derivative,
.
That is,
Assume . Then, integrating both sides of the above and then using Cartan's formula and the differentiation under the integral sign, we get: for ,
where the integration means the integration of each coefficient in a differential form. Letting , we then have:
with the notation
Now, assume is an open ball with center ; then we can take . Then the above formula becomes:
,
which proves the Poincaré lemma when is closed.
Proof in the two-dimensional case
In two dimensions the Poincaré lemma can be proved directly for closed 1-forms and 2-forms as follows.
If is a closed 1-form on , then . If then and . Set
so that . Then must satisfy and . The right hand side here is independent of x since its partial derivative with respect to x is 0. So
and hence
Similarly, if then with . Thus a solution is given by and
Inductive proof
It is also possible to give an inductive proof of Poincaré's lemma which does not use homotopical arguments. Let , where , be the m dimensional coordinate cube. For a differential k-form , let its codegree be the integer m-k. The induction is performed over the codegree of the form. Since we are working over a coordinate domain, partial derivatives and also integrals with respect to the coordinates can be applied to a form itself, by applying them to the coefficients of the form with respect to the canonical coordinates.
First let , i.e. the codegree is 0. It can be written as so if we define by , we havehence, is a primitive of .
Let now , where , i.e. has codegree m-k, and let us suppose that whenever a closed form has codegree less than m-k, the form is exact. The form can be decomposed aswhere neither nor contain any factor of . Define , then , where does not contain any factor of , hence, defining , this form is also closed, but does not involve any factor of . Since this form is closed, we havewhere the last term does not contain a factor of . Due to linear independence of the coordinate differentials, this equation implies thati.e. the form is a differential form in the variables only, hence can be interpreted as an element of , and its codegree is thus m-k-1. The induction hypothesis applies, thus for some , thereforeconcluding the proof for a coordinate cube. In any manifold, every point has a neighborhood which is diffeomorphic to a coordinate cube, the proof also implies that on a manifold any closed k-form (for ) is locally exact.
Implication for de Rham cohomology
By definition, the k-th de Rham cohomology group of an open subset U of a manifold M is defined as the quotient vector space
Hence, the conclusion of the Poincaré lemma is precisely that if is an open ball, then for . Now, differential forms determine a cochain complex called the de Rham complex:
where n = the dimension of M and denotes the sheaf of differential k-forms; i.e., consists of k-forms on U for each open subset U of M. It then gives rise to the complex (the augmented complex)
where is the constant sheaf with values in ; i.e., it is the sheaf of locally constant real-valued functions and the inclusion.
The kernel of is , since the smooth functions with zero derivatives are locally constant. Also, a sequence of sheaves is exact if and only if it is so locally. The Poincaré lemma thus says the rest of the sequence is exact too (since a manifold is locally diffeomorphic to an open subset of and then each point has an open ball as a neighborhood). In the language of homological algebra, it means that the de Rham complex determines a resolution of the constant sheaf . This then implies the de Rham theorem; i.e., the de Rham cohomology of a manifold coincides with the singular cohomology of it (in short, because the singular cohomology can be viewed as a sheaf cohomology.)
Once one knows the de Rham theorem, the conclusion of the Poincaré lemma can then be obtained purely topologically. For example, it implies a version of the Poincaré lemma for contractible or simply connected open sets (see §Simply connected case).
Simply connected case
Especially in calculus, the Poincaré lemma is stated for a simply connected open subset . In that case, the lemma says that each closed 1-form on U is exact. This version can be seen using algebraic topology as follows. The rational Hurewicz theorem (or rather the real analog of that) says that since U is simply connected. Since is a field, the k-th cohomology is the dual vector space of the k-th homology . In particular, By the de Rham theorem (which follows from the Poincaré lemma for open balls), is the same as the first de Rham cohomology group (see §Implication to de Rham cohomology). Hence, each closed 1-form on U is exact.
Poincaré lemma with compact support
There is a version of Poincaré lemma for compactly supported differential forms:
The pull-back along a proper map preserve compact supports; thus, the same proof as the usual one goes through.
Complex-geometry analog
On complex manifolds, the use of the Dolbeault operators and for complex differential forms, which refine the exterior derivative by the formula , lead to the notion of -closed and -exact differential forms. The local exactness result for such closed forms is known as the Dolbeault–Grothendieck lemma (or -Poincaré lemma); cf. . Importantly, the geometry of the domain on which a -closed differential form is -exact is more restricted than for the Poincaré lemma, since the proof of the Dolbeault–Grothendieck lemma holds on a polydisk (a product of disks in the complex plane, on which the multidimensional Cauchy's integral formula may be applied) and there exist counterexamples to the lemma even on contractible domains. The -Poincaré lemma holds in more generality for pseudoconvex domains.
Using both the Poincaré lemma and the -Poincaré lemma, a refined local -Poincaré lemma can be proven, which is valid on domains upon which both the aforementioned lemmas are applicable. This lemma states that -closed complex differential forms are actually locally -exact (rather than just or -exact, as implied by the above lemmas).
Relative Poincaré lemma
The relative Poincaré lemma generalizes Poincaré lemma from a point to a submanifold (or some more general locally closed subset). It states: let V be a submanifold of a manifold M and U a tubular neighborhood of V. If is a closed k-form on U, k ≥ 1, that vanishes on V, then there exists a (k-1)-form on U such that and vanishes on V.
The relative Poincaré lemma can be proved in the same way the original Poincaré lemma is proved. Indeed, since U is a tubular neighborhood, there is a smooth strong deformation retract from U to V; i.e., there is a smooth homotopy from the projection to the identity such that is the identity on V. Then we have the homotopy formula on U:
where is the homotopy operator given by either Lie derivatives or integration along fibers. Now, and so . Since and , we get ; take . That vanishes on V follows from the definition of J and the fact . (So the proof actually goes through if U is not a tubular neighborhood but if U deformation-retracts to V with homotopy relative to V.)
On polynomial differential forms
In characteristic zero, the following Poincaré lemma holds for polynomial differential forms.
Let k be a field of characteristic zero, the polynomial ring and the vector space with a basis written as . Then let be the p-th exterior power of over . Then the sequence of vector spaces
is exact, where the differential is defined by the usual way; i.e., the linearity and
This version of the lemma is seen by a calculus-like argument. First note that , clearly. Thus, we only need to check the exactness at . Let be a -form. Then we write
where the 's do not involve . Define the integration in by the linearity and
which is well-defined by the char zero assumption. Then let
where the integration is applied to each coefficient in . Clearly, the fundamental theorem of calculus holds in our formal setup and thus we get:
where does not involve . Hence, does not involve . Replacing by , we can thus assume does not involve . From the assumption , it easily follows that each coefficient in is independent of ; i.e., is a polynomial differential form in the variables . Hence, we are done by induction.
Remark: With the same proof, the same results hold when is the ring of formal power series or the ring of germs of holomorphic functions. A suitably modified proof also shows the -Poincaré lemma; namely, the use of the fundamental theorem of calculus is replaced by Cauchy's integral formula.
On singular spaces
The Poincaré lemma generally fails for singular spaces. For example, if one considers algebraic differential forms on a complex algebraic variety (in the Zariski topology), the lemma is not true for those differential forms. One way to resolve this is to use formal forms and the resulting algebraic de Rham cohomology can compute a singular cohomology.
However, the variants of the lemma still likely hold for some singular spaces (precise formulation and proof depend on the definitions of such spaces and non-smooth differential forms on them.) For example, Kontsevich and Soibelman claim the lemma holds for certain variants of different forms (called PA forms) on their piecewise algebraic spaces.
The homotopy invariance fails for intersection cohomology; in particular, the Poincaré lemma fails for such cohomology.
Footnote
Notes
References
Further reading
https://mathoverflow.net/questions/287385/p-adic-poincaré-lemma
Differential forms
Lemmas in analysis
Henri Poincaré | Poincaré lemma | [
"Mathematics",
"Engineering"
] | 3,107 | [
"Theorems in mathematical analysis",
"Tensors",
"Differential forms",
"Lemmas in mathematical analysis",
"Lemmas"
] |
600,055 | https://en.wikipedia.org/wiki/Cahit%20Arf | Cahit Arf (; 24 October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasse–Arf theorem in ramification theory, Arf semigroups and Arf rings.
Biography
Cahit Arf was born on 11 October 1910 in Thessaloniki, which was then a part of the Ottoman Empire. His family migrated to Istanbul with the outbreak of the Balkan War in 1912. The family finally settled in İzmir where Cahit Arf received his primary education. Upon receiving a scholarship from the Turkish Ministry of Education he continued his education in Paris and graduated from École Normale Supérieure.
Returning to Turkey, he taught mathematics at Galatasaray High School. In 1933 he joined the Mathematics Department of Istanbul University. In 1937 he went to Göttingen, where he received his PhD from the University of Göttingen and worked with Helmut Hasse and Josue Cruz de Munoz. He returned to Istanbul University and worked there until his involvement with the foundation work of the Scientific and Technological Research Council (TÜBİTAK) upon President Cemal Gürsel's appointment in 1962. After serving as the founding director of the council in 1963, he joined the Mathematics Department of Robert College in Istanbul. Arf spent the period of 1964–1966 working at the Institute for Advanced Study in Princeton, New Jersey. He later visited University of California, Berkeley for one year.
Upon his final return to Turkey, he joined the Mathematics Department of the Middle East Technical University and continued his studies there until his retirement in 1980. Arf received numerous awards for his contributions to mathematics, among them are: İnönü Award in 1948, Scientific and Technological Research Council of Turkey (TÜBİTAK) Science Award in 1974, and Commandeur des Palmes Academiques (France) in 1994. Arf was a member of the Mainz Academy and the Turkish Academy of Sciences. He was the president of the Turkish Mathematical Society from 1985 until 1989. Arf died on December 26, 1997, in Bebek, Istanbul, at the age of 87. His collected works were published, in 1988, by the Turkish Mathematical Society.
Influence
Arf's influence on science in general and mathematics in particular was profound. Although he had very few formal students, many of the mathematicians of Turkey, at some time of their careers, had fruitful discussions on their field of interest with him and had received support and encouragement.
He facilitated the now-celebrated visit of Robert Langlands to Turkey (now famous for the Langlands program, among many other things); during which Langlands worked out some arduous calculations on the epsilon factors of Artin L-functions.
Arf's portrait is depicted on the reverse of the Turkish 10 lira banknote issued in 2009.
Middle East Technical University Department of Mathematics organizes a special lecture session called the Cahit Arf lecture each year in memory of Arf.
Legacy
Since 2001, the Arf lectures in honor of Cahit Arf have been held annually at the Cahit Arf Auditorium in the Department of Mathematics of Middle East Technical University. Each lecture is presented by a distinguished mathematician selected by the advisory board. Since 2006, the Arf Lecturers are invited to deliver their talks at Istanbul Center for Mathematical Sciences (IMBM), too.
2022: Andrew Sutherland of the Massachusetts Institute of Technology
2019: Geordie Williamson of The University of Sydney
2018: Fernando Rodriguez Villegas of The Abdus Salam International Centre for Theoretical Physics
2015: Vladimir Voevodsky of Institute for Advanced Study, Princeton
2013/14: Persi Diaconis of Stanford University
2012: David Nadler of Northwestern University and University of California, Berkeley
2011: Jonathan Pila of University of Oxford
2010: John W Morgan of Simons Center for Geometry and Physics at Stony Brook University
2009: Ben Joseph Green of University of Cambridge
2008: Günter Harder of Mathematisches Institut der Universitat Bonn and Max Planck Institute for Mathematics
2007: Hendrik Lenstra of Universiteit Leiden Mathematisch Instituut
2006: Jean-Pierre Serre of Collège de France
2005: Peter Sarnak of Princeton University and the Institute for Advanced Study, Princeton
2004: Robert Langlands of the Institute for Advanced Study, Princeton
2003: David Mumford of Brown University Division of Applied Mathematics
2002: Don Zagier of University of Utrecht / Collège de France
2001: Gerhard Frey of University of Essen Institute for Experimental Mathematics
See also
Hasse–Arf theorem
Arf invariant
Arf semigroup
Arf ring
Notes
References
Further reading
External links
Cahit Arf Lectures homepage
Page and links on Cahit Arf
A documentary on Cahit Arf
Author profile in the database zbMATH
1910 births
1997 deaths
Scientists from Thessaloniki
People from Salonica vilayet
Macedonian Turks
20th-century Turkish mathematicians
Topologists
École Normale Supérieure alumni
Academic staff of Istanbul University
Institute for Advanced Study visiting scholars
University of Göttingen alumni
Academic staff of Middle East Technical University
Commandeurs of the Ordre des Palmes Académiques
Recipients of TÜBİTAK Science Award
METU Mustafa Parlar Foundation Science Award winners | Cahit Arf | [
"Mathematics"
] | 1,060 | [
"Topologists",
"Topology"
] |
600,171 | https://en.wikipedia.org/wiki/Mary%20Somerville | Mary Somerville ( ; , formerly Greig; 26 December 1780 – 29 November 1872) was a Scottish scientist, writer, and polymath. She studied mathematics and astronomy, and in 1835 she and Caroline Herschel were elected as the first female Honorary Members of the Royal Astronomical Society.
When John Stuart Mill organized a massive petition to Parliament to give women the right to vote, he made sure that the first signature on the petition would be Somerville's.
When she died in 1872, The Morning Post declared in her obituary that "Whatever difficulty we might experience in the middle of the nineteenth century in choosing a king of science, there could be no question whatever as to the queen of science". One of the earliest uses of the word scientist was in a review by William Whewell of Somerville's second book On the Connexion of the Physical Sciences. However, the word was not used to describe Somerville herself; she was known and celebrated as a mathematician or a philosopher.
Somerville College, a college of the University of Oxford, is named after her, reflecting the virtues of liberalism and academic success that the college wished to embody. She is featured on the front of the Royal Bank of Scotland polymer £10 note launched in 2017 along with a quotation from her work On the Connection of the Physical Sciences.
Early life and education
Somerville, the daughter of Vice-Admiral Sir William George Fairfax, was related to several prominent Scottish houses through her mother, Margaret Charters. She was born at the manse of Jedburgh, the home of her maternal aunt and the Rev. Dr. Thomas Somerville (1741–1830) (author of My Own Life and Times). Her childhood home was at Burntisland, Fife, where her mother was from.
Somerville was the second of four surviving children (three of her siblings had died in infancy). She was particularly close to her oldest brother Sam. The family lived in genteel poverty as her father's naval pay remained meagre, despite his rise through the ranks. Her mother supplemented the household's income by growing vegetables, maintaining an orchard and keeping cows for milk. Her mother taught her to read the Bible and Calvinist catechisms. When her household chores were done Mary was free to roam among the birds and flowers in the garden.
In her autobiography Somerville recollects that on her father's return from sea he said to his wife, "This kind of life will never do, Mary must at least know how to write and keep accounts". Ten-year-old Mary was then sent to an expensive boarding school in Musselburgh, where she learned the first principles of writing, rudimentary French and English grammar. Upon returning home, she:
During bad weather Somerville occupied herself with reading the books in her father's library, including Shakespeare, as well as with "domestic duties." Such duties "occupied a great part of my time; besides, I had to shew my sampler, working the alphabet from A to Z, as well as the ten numbers, on canvas". Her aunt Janet came to live with the family and reportedly said to her mother "I wonder you let Mary waste her time in reading, she never shews [sews] more than if she were a man." Somerville was then sent to the village school to learn plain needlework, where she found herself annoyed that her "turn for reading was so much disapproved of, and thought it unjust that women should have been given a desire for knowledge if it were wrong to acquire it." Several times each week the village school master came to teach Mary at home. In her Personal Recollections Somerville notes that the boys learned Latin at the village school, while "it was thought sufficient for the girls to be able to read the Bible; very few even learnt writing."
At age 13 her mother sent her to writing school in Edinburgh, where she improved her writing skills and studied arithmetic. Back in Burntisland she taught herself sufficient Latin to read the books in the home library. While visiting her aunt in Jedburgh she met her uncle, Dr. Thomas Somerville. She gathered her courage to tell him that she had been learning Latin. Dr. Somerville assured her that in earlier times many women had become elegant scholars. He then proceeded to enable her to improve her Latin by reading Virgil with her. While staying with another uncle, William Charters, in Edinburgh, Somerville was sent to a dancing school, where she learned manners and how to curtsey. She also accompanied her uncle and aunt on their visits to the Lyell family in Kinnordy; Charles Lyell later became a celebrated geologist and Somerville's friend.
Somerville's father was a Tory, but she was a Liberal, made so by the "unjust and exaggerated abuse of the Liberal party. From my earliest years my mind revolved against oppression and tyranny, and I resented the injustice of the world in denying all those privileges of education to my sex which were so lavishly bestowed on men." At the time, slaves still worked to harvest sugar in the West Indies and in protest Somerville and her oldest brother Sam would refuse to take sugar in their tea.
At Burntisland, where she stayed the summer with her uncle and aunt, Somerville had access to elementary books on algebra and geometry. She spent the summer learning to play the piano. In addition to the piano she learned Greek so she could read Xenophon and Herodotus in their original versions. On her return to Edinburgh she was allowed to attend the academy of painter Alexander Nasmyth, which had opened for ladies. When Nasmyth advised another student to study Euclid's Elements to gain a foundation in perspective, astronomy and mechanical science, Somerville spotted an opportunity. She thought the book would help her understand Navigations by John Robertson.
She continued in the traditional role of a daughter in a well-connected family, attending social events and maintaining a sweet and polite manner, which led to her nickname as "the Rose of Jedburgh" among Edinburgh socialites. Meanwhile, a young tutor came to stay with the family in Burntisland to educate her younger brother Henry. The tutor, Mr. Craw, was a Greek and Latin scholar, and Somerville asked him to purchase elementary books on algebra and geometry for her. He presented Somerville with Euclid's Elements and Algebra by John Bonnycastle. Somerville would rise early to play the piano, painted during the day, and stayed up late to study Euclid and algebra. When Lord Balmuto, a family friend, invited her to visit his family, Somerville saw her first laboratory. She also spent some time with the Oswalds family in Dunnikeir, whose daughter, a bold horsewoman who impressed Somerville, became a Greek and Latin scholar and married Thomas Bruce, 7th Earl of Elgin.
Winters were usually spent in Edinburgh. In the winter of 1796 Somerville made her first appearance at a ball under the care of Lady Burchan. Her first dancing partner was the Earl of Minto.
In the autumn of 1797 her father was caught up in a mutiny while serving as flag-captain under Admiral Duncan on . Despite the mutiny, the Battle of Camperdown was won by the British. Her father was knighted and made Colonel of Marines. Her eldest brother died at the age of 21 in Calcutta while serving in the East India Company's military service. The family had hoped he would make a sufficient fortune in a few years to enable him to return home.
Marriage and studies
In 1804 Somerville met her first husband, Lieutenant Samuel Greig. Her distant cousin, a son of Admiral Samuel Greig, he was commissioner of the Russian navy and Russian consul for Britain. They married and had two children, one of whom, Woronzow Greig, would become a barrister and scientist. They lived in London, but it was not a happy time for Somerville. Her husband did not think much of women's intellectual capacity. Indeed, Greig "possessed in full the prejudice against learned women which was common at that time." Instead, Somerville took lessons in French, which was considered more appropriate. When her husband died in 1807 she was still nursing their youngest child and she returned to Scotland.
Her inheritance from Greig gave her the freedom to pursue intellectual interests. By that time she had studied plane and spherical trigonometry, conic sections and James Ferguson's Astronomy. Somerville also read Isaac Newton's Principia. John Playfair, professor of natural philosophy at University of Edinburgh, encouraged her studies and through him she began a correspondence with William Wallace, with whom she discussed mathematical problems.
Somerville began solving mathematical problems posed in the mathematical journal of the Military College at Marlow and eventually made a name for herself after solving a diophantine problem, for which she was awarded a silver medal in 1811. Somerville published five solutions in Volumes 3 and 4 of the Mathematical Repository under the pseudonym 'A Lady'. Two of her solutions demonstrated her early adoption of differential calculus—her contribution to the circulation and visibility of calculus in early 19th-century Britain.
Wallace suggested that she study the writings of French mathematician Pierre-Simon Laplace, which summarised the theory of gravity and collected the mathematical results established in the 50 years since Principia had been published. Somerville said that studying Laplace's work gave her the confidence to persevere in her mathematical studies. She extended her studies to astronomy, chemistry, geography, microscopy, electricity and magnetism. At the age of 33 she bought herself a library of scientific books. These included Louis-Benjamin Francœur's Elements of Mechanics, Sylvestre François Lacroix' Algebra and Calculus Treatise, Jean-Baptiste Biot's Analytical Geometry and Astronomy, Siméon Denis Poisson's Treatise on Mechanics, Joseph-Louis Lagrange's Theory of Analytical Functions, Leonhard Euler's Elements of Algebra and Isoperimetrical Problems, Alexis Clairaut's Figure of the Earth, Gaspard Monge's Application of Analysis to Geometry, and François Callet's Logarithmus.
In her Personal Recollections Somerville expressed the opinion that mathematical science was at a low ebb in Britain, due to a reverence for Newton that prevented scientists from adopting calculus. On the Continent astronomical and mechanical science had reached a high degree of perfection. In her opinion this deadlock was not broken until 1816, when Charles Babbage, John Herschel and George Peacock published a translation of the lectures of Sylvestre Lacroix, then a state-of-the-art calculus textbook.
While staying with her family in Scotland, Somerville became acquainted with several leading intellectual lights, such as Henry Brougham. In 1812 she married another cousin, Dr William Somerville (1771–1860), inspector of the Army Medical Board, with whom she had four children. He encouraged and aided her in the study of the physical sciences. In 1817 her husband was elected to the Royal Society and together they moved in the leading social circles of the day. Somerville was well known to scientists, as well as to leading writers and artists. Painter J. M. W. Turner knew that Somerville and her husband's family were neighbors of the writer Walter Scott. She wrote, "I shall never forget the charm of this little society, especially the supper-parties at Abbotsford, when Scott was in the highest glee, telling amusing tales, ancient legends, ghost and witch stories."
In 1819 Somerville's husband was appointed physician to Chelsea Hospital and the family moved into a government house at Hanover Square. Somerville was a friend of Anne Isabella Milbanke, Baroness Wentworth, and was mathematics tutor to her daughter, Ada Lovelace. With Somerville, Lovelace attended scientific gatherings where she met Charles Babbage. Somerville College owns a letter from Babbage to Somerville inviting her to view his 'Calculating Engine'. Somerville frequently visited Babbage while he was "making his Calculating-machines". Somerville and Lovelace maintained a close friendship and when Lovelace encountered difficulties with a mathematical calculation, she would walk to Somerville's house and discuss the matter over a cup of tea.
In 1823 the Somervilles' youngest daughter died after an illness.
While living in London the Somervilles travelled through Europe on a number of occasions, leaving their children with their German governess. Among their travel companions was the jurist and politician Sir James Mackintosh. Before leaving London the Somervilles contacted the people they wanted to meet, which included numerous celebrated intellectuals. The Somervilles also received frequent visitors; writer Maria Edgeworth would visit them when in England.
Science practice and writing
Somerville conducted experiments to explore the relationship between light and magnetism. Her first paper, "The magnetic properties of the violet rays of the solar spectrum", was published in the Proceedings of the Royal Society in 1826. Although her conclusions were faulty, the topic was of popular interest at the time and the paper brought her to notice in scientific circles. Using a sample of silver nitrate supplied by Michael Faraday, Somerville conducted experiments on the blackening effect of sunlight, the reaction used in early experiments in photography. She later developed her technique by using an optical prism and vegetable dyes, producing an early version of the optical spectrometer. Sir David Brewster, inventor of the kaleidoscope, wrote in 1829 that Mary Somerville was "certainly the most extraordinary woman in Europe – a mathematician of the very first rank with all the gentleness of a woman".
Lord Brougham asked Somerville to translate the Mécanique Céleste of Pierre-Simon Laplace for the Society for the Diffusion of Useful Knowledge. Laplace had, in five exhaustive volumes, summed up the current state of gravitational mathematics. Mécanique Céleste was acclaimed as the greatest intellectual achievement since the Principia. Somerville produced not just a translation, but also an expanded version of the first two volumes. She wrote a standalone exposition of the mathematics behind the workings of the Solar System, of which she said "I translated Laplace's work from algebra into common language". It was published in 1831, under the title of The Mechanism of the Heavens, and it immediately made her famous. Until the 1880s Mechanism was set as a textbook for undergraduates at the University of Cambridge.
After receiving a copy of Mechanism Joanna Baillie wrote to Somerville, "I feel myself greatly honoured by receiving such a mark of regard from one who has done more to remove the light estimation in which the capacity of women is too often held than all that has been accomplished by the whole Sisterhood of Poetical Damsels & novel-writing Authors." The book was praised by George Peacock, Professor of the University of Cambridge, thus many of the 750 copies printed were bought in Cambridge. Reviews were favourable and Somerville received letters of congratulation from "many men of science". She was elected honorary member of the Royal Irish Academy, the Bristol Philosophical Institution, and the Société de Physique et d'Histoire Naturelle de Genève in 1834. The British Crown granted her a civil pension of £200 a year in recognition of her eminence in science and literature.
Somerville was passionate about astronomy and believed it to be the most extensive example of the connection of the physical sciences in that it combined the sciences of number and quantity, of rest and motion.
In Somerville's time the value of scientific publications depended on the currency of the information, therefore frequent editions had to be produced. Her subsequent books reflect the time that she could be free in her domestic life as her children became more independent. They also reflect the need to earn money, as the Somervilles suffered through a number of financial crises that peaked in 1835. She publicly and plausibly maintained that she wrote only for pleasure. Privately she paid considerable attention to the profitability of her books. Through personal connections she could secure John Murray as the publisher of her first book, Mechanism, and he remained her publisher throughout her long career. Murray later commented that despite having made little profit he was very pleased to have had the honour of publishing the works of such an extraordinary person. Her second book, On the Connexion of the Physical Sciences, sold 15,000 copies and established her reputation in elite science.She was among those who discussed a hypothetical planet perturbing Uranus. In the 6th edition of Connexion (1842) she wrote, "If after the lapse of years the tables formed from a combination of numerous observations should be still inadequate to represent the motions of Uranus, the discrepancies may reveal the existence, nay, even the mass and orbit of a body placed for ever beyond the sphere of vision". Predictions were fulfilled in 1846 with the discovery of Neptune revolving at a distance of 3,000,000,000 miles from the Sun. "The mass of Neptune, the size and position of his orbit in space, and his periodic time, were determined from his disturbing action on Uranus before the planet itself had been seen." Connexion ran to 10 editions, more than 9,000 copies and was its publisher's most successful science book until The Origin of Species by Charles Darwin. It was translated into German and Italian and went through various editions in the United States.
Her book Physical Geography was published in 1848 and was the first English textbook on the subject. It remained in use until the early 20th century. Physical Geography was financially successful and brought her the Victoria Gold Medal of the Royal Geographical Society. Somerville followed, as she said, "the noble example of Baron Humboldt, the patriarch of physical geography", and she took an extended view of geography that included the Earth, its animal, "vegetable inhabitants", as well as "the past and present condition of man, the origin, manners, and languages of existing nations, and the monuments of those that have been".
Physical Geography starts with describing the overall structure of planet Earth, along with a brief allusion to the location of the Earth within the Solar System. Subsequently, the book focuses on terrestrial topics, such as the most basic features of land and water, and formations such as mountains, volcanoes, oceans, rivers and lakes. Somerville goes on to discuss the elements that govern temperature, such as light, electricity, storms, the aurora and magnetism. Eventually the book turns to vegetation, birds and mammals, and their geographical distribution in the Arctic, Europe, Asia, Africa, America and the Antarctic. Somerville ends the book with a discussion of "the distribution, condition, and future prospects of the human race". She emphasises the reciprocal dependencies in physical geography and the relationship between human beings and nature. In line with Victorian thinking, Somerville asserts the superiority of human beings, but maintains the interdependencies and interconnectedness of creation. Physical Geography sold more copies than any of her other books and earned Humboldt's admiration. After receiving a copy of the book he wrote to her: "You alone could provide your literature with an original cosmological work".
Her fourth book, Molecular and Microscopic Science, took 10 years to write. Published in 1869, she soon had doubts about devoting herself to popularising science, instead of concentrating on mathematics alone. Of the book she said: "In writing this book I made a great mistake, and repent it - Mathematics are the natural bent of my mind. If I had devoted myself exclusively to that study, I might probably have written something useful, as a new era had begun in that science." Regardless, the book was another success. It gave an up-to-date description of the latest discoveries revealed through the microscope and was published in two volumes and three parts. In the first part Somerville explained the latest thinking on atoms and molecules, the second covered plant life, while the third explored animal life. The book included 180 illustrations, which caused her publisher great expense.
She was elected to the American Geographical and Statistical Society in 1857 and the Italian Geographical Society in 1870, and was made a member of the American Philosophical Society.
Death
From 1833 onwards Somerville and her husband spent most of their time in Italy. Somerville maintained correspondence with a large number of leading scientists and remained engaged in current debates on facts and theories.
In 1868, four years before her death at 91, she was the first person to sign John Stuart Mill's unsuccessful petition for female suffrage. In her autobiography Somerville wrote that "British laws are adverse to women". She detailed the obstacles she had faced in obtaining an education as a young girl, though she did not speculate on the nature of the problem. During her lifetime agitation had grown for women's access to higher education. In 1875 astronomer Maria Mitchell was told by a college president that he "would hire a woman scientist if she was as good as Mary Somerville".
Somerville died at Naples on 29 November 1872, and was buried there in the English Cemetery.
Legacy
In the year following Somerville's death, her autobiographical Personal Recollections was published, consisting of reminiscences written during her old age. Over 10,000 pages are in the Somerville Collection of the Bodleian Library and Somerville College, Oxford. The collection includes papers relating to her writing and published work, and correspondence with family members, scientists and writers, as well as other figures in public life. Also included is substantial correspondence with the Byron and Lovelace families.
Her shell collection was given to Somerville College, Oxford by her descendants.
Somerville Square in Burntisland is named after her family and marks the site of their home.
Somerville College, Oxford, was named after Somerville, as are Somerville House, Burntisland, where she lived for a time, and Somerville House, a high school for girls in Brisbane, Australia. One of the Committee Rooms of the Scottish Parliament in Edinburgh has been named after her.
Somerville Island (), a small island in Barrow Strait, Nunavut, was named after her by Sir William Edward Parry in 1819.
The Somerville Club was founded in 1878 in London, by 1887 it was re-established as the New Somerville Club, and it disappeared by 1908.
The vessel was launched in 1835 at Liverpool. She traded with India for Taylor, Potter & Co., of Liverpool, and disappeared with the loss of all aboard in late 1852 or early 1853.
Mary Somerville is featured in miniature in The English Bijou Almanack, 1837, with poetry by Letitia Elizabeth Landon.
5771 Somerville (1987 ST1) is a main-belt asteroid discovered on 21 September 1987 by E. Bowell at Lowell Observatory in Flagstaff, Arizona, and named after her. Somerville crater is a small lunar crater in the eastern part of the Moon. It lies to the east of the prominent crater Langrenus. It is one of a handful of lunar craters named after women.
In February 2016 Somerville was shortlisted, along with Scottish physicist James Clerk Maxwell and civil engineer Thomas Telford, in a public competition run by the Royal Bank of Scotland to decide whose face should appear on the bank's new £10 notes, to be issued in 2017. Later that month RBS announced that she had won the public vote, held on Facebook. The banknotes, bearing her image, were issued in the second half of 2017.
On 2 February 2020, Google celebrated her with a Google Doodle.
On 1 April 2022, a satellite named after Somerville (ÑuSat 26, COSPAR 2022–033) was launched into space as part of the Satellogic Aleph-1 satellite constellation.
Children
From her first marriage she had a son, Woronzow Greig (1805–1865), named after Count Semyon Vorontsov, the Russian ambassador in London who had appointed Samuel Greig as his Consul General. Woronzow married Agnes Graham but all their children died at birth or in infancy.
From her second marriage she had three daughters and one son: Margaret Farquhar Somerville (1813–1823; died in childhood), Thomas Somerville (1814–1815; died in infancy), Martha Charters Somerville (1815–1879) and Mary Charlotte Somerville (1817–1875). Her two surviving daughters spent most of their lives caring for Mary.
Bibliography
1826 "On the magnetizing power of the more refrangible solar rays"
1831 Mechanism of the Heavens
1832 "A Preliminary Dissertation on the Mechanisms of the Heavens"
1834 On the Connection of the Physical Sciences
1848 Physical Geography
1869 Molecular and Microscopic Science
1874 Personal recollections, from early life to old age, of Mary Somerville
See also
People on Scottish banknotes
Timeline of women in science
– ship launched at Liverpool in 1835 and named for Mary Somerville
Notes
References
. Digitised 2007, original in Harvard University. Reprinted by AMS Press (January 1996), . Written by her daughter.
Neeley, Kathryn A. Mary Somerville: Science, Illumination, and the Female Mind, Cambridge & New York: Cambridge University Press, 2001.
External links
"Mary Fairfax Somerville", Biographies of Women Mathematicians, Agnes Scott College
Mary Somerville, an article by Maria Mitchell, Atlantic Monthly 5 (May 1860), 568–571.
Bibliography from the Astronomical Society of the Pacific
Catalogue of correspondence and papers of Mary Somerville and of the Somerville and related families, c.1700–1972, held at the Bodleian Library, University of Oxford
Scottish astronomers
Scottish science writers
1780 births
1872 deaths
Scottish suffragists
19th-century Scottish translators
Scottish translators
Fairfax family
Women astronomers
Royal Astronomical Society
Members of the American Philosophical Society
People from Burntisland
People from Jedburgh
Scottish expatriates in Italy
19th-century British astronomers
19th-century Scottish mathematicians
19th-century Scottish women scientists
19th-century Scottish writers
19th-century Scottish women writers
19th-century British women mathematicians | Mary Somerville | [
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"Women astronomers",
"Astronomers"
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600,368 | https://en.wikipedia.org/wiki/Shelf%20life | Shelf life is the length of time that a commodity may be stored without becoming unfit for use, consumption, or sale. In other words, it might refer to whether a commodity should no longer be on a pantry shelf (unfit for use), or no longer on a supermarket shelf (unfit for sale, but not yet unfit for use). It applies to cosmetics, foods and beverages, medical devices, medicines, explosives, pharmaceutical drugs, chemicals, tyres, batteries, and many other perishable items. In some regions, an advisory best before, mandatory use by or freshness date is required on packaged perishable foods. The concept of expiration date is related but legally distinct in some jurisdictions.
Background
Shelf life is the recommended maximum time for which products or fresh (harvested) produce can be stored, during which the defined quality of a specified proportion of the goods remains acceptable under expected (or specified) conditions of distribution, storage and display.
According to the United States Department of Agriculture (USDA), "canned foods are safe indefinitely as long as they are not exposed to freezing temperatures, or temperatures above 90 °F (32.2 °C)". If the cans look okay, they are safe to use. Discard cans that are dented, rusted, or swollen. High-acid canned foods (tomatoes, fruits) will keep their best quality for 12 to 18 months; low-acid canned foods (meats, vegetables) for 2 to 5 years.
"Sell by date" is a less ambiguous term for what is often referred to as an "expiration date". Most food is still edible after the expiration date. A product that has passed its shelf life might still be safe, but quality is no longer guaranteed. In most food stores, waste is minimized by using stock rotation, which involves moving products with the earliest sell by date from the warehouse to the sales area, and then to the front of the shelf, so that most shoppers will pick them up first and thus they are likely to be sold before the end of their shelf life. Some stores can be fined for selling out of date products; most if not all would have to mark such products down as wasted, resulting in a financial loss.
Shelf life depends on the degradation mechanism of the specific product. Most can be influenced by several factors: exposure to light, heat, moisture, transmission of gases, mechanical stresses, and contamination by things such as micro-organisms. Product quality is often mathematically modelled around a parameter (concentration of a chemical compound, a microbiological index, or moisture content).
For some foods, health issues are important in determining shelf life. Bacterial contaminants are ubiquitous, and foods left unused too long will often be contaminated by substantial amounts of bacterial colonies and become dangerous to eat, leading to food poisoning. However, shelf life alone is not an accurate indicator of how long the food can safely be stored. For example, pasteurized milk can remain fresh for five days after its sell-by date if it is refrigerated properly. However, improper storage of milk may result in bacterial contamination or spoilage before the expiration date.
Pharmaceuticals
The expiration date of pharmaceuticals specifies the date the manufacturer guarantees the full potency and safety of a drug. Most medications continue to be effective and safe for a time after the expiration date. A rare exception is a case of renal tubular acidosis purportedly caused by expired tetracycline. A study conducted by the U.S. Food and Drug Administration covered over 100 drugs, prescription and over-the-counter. The study showed that about 90% of them were safe and effective as long as 15 years past their expiration dates. Joel Davis, a former FDA expiration-date compliance chief, said that with a handful of exceptions - notably nitroglycerin, insulin and some liquid antibiotics - most expired drugs are probably effective.
Shelf life is not significantly studied during drug development, and drug manufacturers have economic and liability incentives to specify shorter shelf lives so that consumers are encouraged to discard and repurchase products. One major exception is the Shelf Life Extension Program (SLEP) of the U.S. Department of Defense (DoD), which commissioned a major study of drug efficacy from the FDA starting in the mid-1980s. One criticism is that the U.S. Food and Drug Administration (FDA) refused to issue guidelines based on SLEP research for normal marketing of pharmaceuticals even though the FDA performed the study. The SLEP and FDA signed a memorandum that scientific data could not be shared with the public, public health departments, other government agencies, and drug manufacturers. State and local programs are not permitted to participate. The failure to share data has caused foreign governments to refuse donations of expired medications. One exception occurred during the 2010 Swine Flu Epidemic when the FDA authorized expired Tamiflu based on SLEP Data. The SLEP discovered that drugs such as Cipro remained effective nine years after their shelf life, and, as a cost-saving measure, the US military routinely uses a wide range of SLEP tested products past their official shelf life if drugs have been stored properly.
Packaging factors
Preservatives and antioxidants may be incorporated into some food and drug products to extend their shelf life. Some companies use induction sealing and vacuum/oxygen-barrier pouches to assist in the extension of the shelf life of their products where oxygen causes the loss.
The DoD Shelf-Life Program defines shelf-life as
The total period of time beginning with the date of manufacture, date of cure (for elastomeric and rubber products only), date of assembly, or date of pack (subsistence only), and terminated by the date by which an item must be used (expiration date) or subjected to inspection, test, restoration, or disposal action; or after inspection/laboratory test/restorative action that an item may remain in the combined wholesale (including manufacture's) and retail storage systems and still be suitable for issue or use by the end user. Shelf-life is not to be confused with service-life (defined as, A general term used to quantify the average or standard life expectancy of an item or equipment while in use. When a shelf-life item is unpacked and introduced to mission requirements, installed into intended application, or merely left in storage, placed in pre-expended bins, or held as bench stock, shelf-life management stops and service life begins.)
Shelf life is often specified in conjunction with a specific product, package, and distribution system. For example, an MRE field ration is designed to have a shelf life of three years at and six months at .
Temperature control
Nearly all chemical reactions can occur at normal temperatures (although different reactions proceed at different rates). However most reactions are accelerated by high temperatures, and the degradation of foods and pharmaceuticals is no exception. The same applies to the breakdown of many chemical explosives into more unstable compounds. Nitroglycerine is notorious. Old explosives are thus more dangerous (i.e. liable to be triggered to explode by very small disturbances, even trivial jiggling) than more recently manufactured explosives. Rubber products also degrade as sulphur bonds induced during vulcanization revert; this is why old rubber bands and other rubber products soften and get crispy, and lose their elasticity as they age.
The often quoted rule of thumb is that chemical reactions double their rate for each temperature increase of because activation energy barriers are more easily surmounted at higher temperatures. However, as with many rules of thumb, there are many caveats and exceptions. The rule works best for reactions with activation energy values around 50 kJ/mole; many of these are important at the usual temperatures we encounter. It is often applied in shelf life estimation, sometimes wrongly. There is a widespread impression, for instance in industry, that "triple time" can be simulated in practice by increasing the temperature by , e.g., storing a product for one month at simulates three months at . This is mathematically incorrect (if the rule was precisely accurate the required temperature increase would be about ), and in any case the rule is only a rough approximation and cannot always be relied on. Chemists often use the more comprehensive Arrhenius equation for better estimations.
The same is true, up to a point, of the chemical reactions of living things. They are usually catalyzed by enzymes which change reaction rates, but with no variation in catalytic action, the rule of thumb is still mostly applicable. In the case of bacteria and fungi, the reactions needed to feed and reproduce speed up at higher temperatures, up to the point that the proteins and other compounds in their cells themselves begin to break down, or denature, so quickly that they cannot be replaced. This is why high temperatures kill bacteria and other micro-organisms: 'tissue' breakdown reactions reach such rates that they cannot be compensated for and the cell dies. On the other hand, 'elevated' temperatures short of these result in increased growth and reproduction; if the organism is harmful, perhaps to dangerous levels.
Just as temperature increases speed up reactions, temperature decreases reduce them. Therefore, to make explosives stable for longer periods, or to keep rubber bands springy, or to force bacteria to slow down their growth, they can be cooled. That is why shelf life is generally extended by temperature control: (refrigeration, insulated shipping containers, controlled cold chain, etc.) and why some medicines and foods must be refrigerated. Since such storing of such goods is temporal in nature and shelf life is dependent on the temperature controlled environment, they are also referred to as cargo even when in special storage to emphasize the inherent time-temperature sensitivity matrix.
Temperature data loggers and time temperature indicators can record the temperature history of a shipment to help estimate their remaining shelf life.
According to the USDA, "foods kept frozen continuously are safe indefinitely".
Packaging
Passive barrier packaging can often help control or extend shelf life by blocking the transmission of deleterious substances, like moisture or oxygen, across the barrier. Active packaging, on the other hand, employs the use of substances that scavenge, capture, or otherwise render harmless deleterious substances. When moisture content is a mechanism for product degradation, packaging with a low moisture vapor transmission rate and the use of desiccants help keep the moisture in the package within acceptable limits. When oxidation is the primary concern, packaging with a low oxygen transmission rate and the use of oxygen absorbers can help extend the shelf life. Produce and other products with respiration often require packaging with controlled barrier properties. The use of a modified atmosphere in the package can extend the shelf life for some products.
Related concepts
The concept of shelf life applies to other products besides food and drugs. Gasoline has a shelf life, although it is not normally necessary to display a sell-by date. Exceeding this time-frame will introduce harmful varnishes, etc. into equipment designed to operate with these products, i.e. a gasoline lawn mower that has not been properly winterized could incur damage that will prevent use in the spring, and require expensive servicing to the carburetor.
Some glues and adhesives also have a limited storage life, and will stop working in a reliable and usable manner if their safe shelf life is exceeded.
Rather different is the use of a time limit for the use of items like vouchers, gift certificates and pre-paid phone cards, so that after the displayed date the voucher etc. will no longer be valid. Bell Mobility and its parent company, BCE Inc. have been served with notice of a $100-million class-action lawsuit alleging that expiry dates on its pre-paid wireless services are illegal.
See also
Accelerated aging
Cold chain
Digital permanence
Expiration date
Failure rate
Food waste
Inventory turnover
Modified atmosphere
Moisture sorption isotherm
Moisture vapor transmission rate
Packaging and labelling
Permeation
Planned obsolescence
Redox
Shelf stable
Yellow sticker
References
Further reading
Includes a list of the many terms used in the United States food industry.
Anonymous, "Cold Chain Management", 2003, 2006
Anonymous, Protecting Perishable Foods During Transport by Truck , USDA Handbook 669, 1995
Kilcast, D., Subramamiam, P., Food and Beverage Stability and Shelf Life, Woodhead Publishing, 2011,
Labuza, T. P., Szybist, L., Open dating of Foods, Food and Nutrition Press, 2001; other edition: Wiley-Blackwell, 2004,
Man, C. M., Jones. A. A., Shelf-Life Evaluation of Foods,
Robertson, G.L., Food Packaging and Shelf Life: A Practical Guide, CRC Press, 2010,
Steele, R., Understanding and Measuring the Shelf-Life of Food, Woodhead Publishing, 2004,
Weenen, H., Cadwallader, K., Freshness and Shelf Life of Foods, ACS, 2002,
External links
USDA - Food Product Dating and storage guidelines
FDA - Food freshness and smart packaging
How to store your food
Food safety
Packaging
Drug safety
Food retailing
Product expiration
Retail processes and techniques | Shelf life | [
"Chemistry"
] | 2,701 | [
"Drug safety"
] |
600,373 | https://en.wikipedia.org/wiki/Gradient%20conjecture | In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France).
The conjecture states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero.
The proof depends on a theorem due to Stanis%C5%82aw %C5%81ojasiewicz.
References
R. Thom (1989) "Problèmes rencontrés dans mon parcours mathématique: un bilan", Publications Math%C3%A9matiques de l%27IH%C3%89S 70: 200 to 214. (This gradient conjecture due to René Thom was in fact well-known among specialists by the early 70's, having been often discussed during that period by Thom during his weekly seminar on singularities at the IHES.)
In 2000 the conjecture was proven correct in Annals of Mathematics 152: 763 to 792. The proof is available here.
Theorems in analysis | Gradient conjecture | [
"Mathematics"
] | 304 | [
"Theorems in mathematical analysis",
"Mathematical analysis",
"Mathematical analysis stubs",
"Mathematical problems",
"Mathematical theorems"
] |
600,500 | https://en.wikipedia.org/wiki/Scenario%20planning | Scenario planning, scenario thinking, scenario analysis, scenario prediction and the scenario method all describe a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and generalization of classic methods used by military intelligence.
In the most common application of the method, analysts generate simulation games for policy makers. The method combines known facts, such as demographics, geography and mineral reserves, with military, political, and industrial information, and key driving forces identified by considering social, technical, economic, environmental, and political ("STEEP") trends.
In business applications, the emphasis on understanding the behavior of opponents has been reduced while more attention is now paid to changes in the natural environment. At Royal Dutch Shell for example, scenario planning has been described as changing mindsets about the exogenous part of the world prior to formulating specific strategies.
Scenario planning may involve aspects of systems thinking, specifically the recognition that many factors may combine in complex ways to create sometimes surprising futures (due to non-linear feedback loops). The method also allows the inclusion of factors that are difficult to formalize, such as novel insights about the future, deep shifts in values, and unprecedented regulations or inventions. Systems thinking used in conjunction with scenario planning leads to plausible scenario storylines because the causal relationship between factors can be demonstrated. These cases, in which scenario planning is integrated with a systems thinking approach to scenario development, are sometimes referred to as "dynamic scenarios".
Critics of using a subjective and heuristic methodology to deal with uncertainty and complexity argue that the technique has not been examined rigorously, nor influenced sufficiently by scientific evidence. They caution against using such methods to "predict" based on what can be described as arbitrary themes and "forecasting techniques".
A challenge and a strength of scenario-building is that "predictors are part of the social context about which they are trying to make a prediction and may influence that context in the process". As a consequence, societal predictions can become self-destructing. For example, a scenario in which a large percentage of a population will become HIV infected based on existing trends may cause more people to avoid risky behavior and thus reduce the HIV infection rate, invalidating the forecast (which might have remained correct if it had not been publicly known). Or, a prediction that cybersecurity will become a major issue may cause organizations to implement more secure cybersecurity measures, thus limiting the issue.
Principle
Crafting scenarios
Combinations and permutations of fact and related social changes are called "scenarios". Scenarios usually include plausible, but unexpectedly important, situations and problems that exist in some nascent form in the present day. Any particular scenario is unlikely. However, futures studies analysts select scenario features so they are both possible and uncomfortable. Scenario planning helps policy-makers and firms anticipate change, prepare responses, and create more robust strategies.
Scenario planning helps a firm anticipate the impact of different scenarios and identify weaknesses. When anticipated years in advance, those weaknesses can be avoided or their impacts reduced more effectively than when similar real-life problems are considered under the duress of an emergency. For example, a company may discover that it needs to change contractual terms to protect against a new class of risks, or collect cash reserves to purchase anticipated technologies or equipment. Flexible business continuity plans with "PREsponse protocols" can help cope with similar operational problems and deliver measurable future value.
Wargames
Strategic military intelligence organizations also construct scenarios. The methods and organizations are almost identical, except that scenario planning is applied to a wider variety of problems than merely military and political problems.
As in military intelligence, the chief challenge of scenario planning is to find out the real needs of policy-makers, when policy-makers may not themselves know what they need to know, or may not know how to describe the information that they really want.
Good analysts design wargames so that policy makers have great flexibility and freedom to adapt their simulated organisations. Then these simulated organizations are "stressed" by the scenarios as a game plays out. Usually, particular groups of facts become more clearly important. These insights enable intelligence organizations to refine and repackage real information more precisely to better serve the policy-makers' real-life needs. Usually the games' simulated time runs hundreds of times faster than real life, so policy-makers experience several years of policy decisions, and their simulated effects, in less than a day.
This chief value of scenario planning is that it allows policy-makers to make and learn from mistakes without risking career-limiting failures in real life. Further, policymakers can make these mistakes in a safe, unthreatening, game-like environment, while responding to a wide variety of concretely presented situations based on facts. This is an opportunity to "rehearse the future", an opportunity that does not present itself in day-to-day operations where every action and decision counts.
How military scenario planning or scenario thinking is done
Decide on the key question to be answered by the analysis. By doing this, it is possible to assess whether scenario planning is preferred over the other methods. If the question is based on small changes or a very small number of elements, other more formalized methods may be more useful.
Set the time and scope of the analysis. Take into consideration how quickly changes have happened in the past, and try to assess to what degree it is possible to predict common trends in demographics, product life cycles. A usual timeframe can be five to 10 years.
Identify major stakeholders. Decide who will be affected and have an interest in the possible outcomes. Identify their current interests, whether and why these interests have changed over time in the past.
Map basic trends and driving forces. This includes industry, economic, political, technological, legal, and societal trends. Assess to what degree these trends will affect your research question. Describe each trend, how and why it will affect the organisation. In this step of the process, brainstorming is commonly used, where all trends that can be thought of are presented before they are assessed, to capture possible group thinking and tunnel vision.
Find key uncertainties. Map the driving forces on two axes, assessing each force on an uncertain/(relatively) predictable and important/unimportant scale. All driving forces that are considered unimportant are discarded. Important driving forces that are relatively predictable (ex. demographics) can be included in any scenario, so the scenarios should not be based on these. This leaves you with a number of important and unpredictable driving forces. At this point, it is also useful to assess whether any linkages between driving forces exist, and rule out any "impossible" scenarios (ex. full employment and zero inflation).
Check for the possibility to group the linked forces and if possible, reduce the forces to the two most important. (To allow the scenarios to be presented in a neat xy-diagram)
Identify the extremes of the possible outcomes of the two driving forces and check the dimensions for consistency and plausibility. Three key points should be assessed:
Time frame: are the trends compatible within the time frame in question?
Internal consistency: do the forces describe uncertainties that can construct probable scenarios.
Vs the stakeholders: are any stakeholders currently in disequilibrium compared to their preferred situation, and will this evolve the scenario? Is it possible to create probable scenarios when considering the stakeholders? This is most important when creating macro-scenarios where governments, large organisations et al. will try to influence the outcome.
Define the scenarios, plotting them on a grid if possible. Usually, two to four scenarios are constructed. The current situation does not need to be in the middle of the diagram (inflation may already be low), and possible scenarios may keep one (or more) of the forces relatively constant, especially if using three or more driving forces. One approach can be to create all positive elements into one scenario and all negative elements (relative to the current situation) in another scenario, then refining these. In the end, try to avoid pure best-case and worst-case scenarios.
Write out the scenarios. Narrate what has happened and what the reasons can be for the proposed situation. Try to include good reasons why the changes have occurred as this helps the further analysis. Finally, give each scenario a descriptive (and catchy) name to ease later reference.
Assess the scenarios. Are they relevant for the goal? Are they internally consistent? Are they archetypical? Do they represent relatively stable outcome situations?
Identify research needs. Based on the scenarios, assess where more information is needed. Where needed, obtain more information on the motivations of stakeholders, possible innovations that may occur in the industry and so on.
Develop quantitative methods. If possible, develop models to help quantify consequences of the various scenarios, such as growth rate, cash flow etc. This step does of course require a significant amount of work compared to the others, and may be left out in back-of-the-envelope-analyses.
Converge towards decision scenarios. Retrace the steps above in an iterative process until you reach scenarios which address the fundamental issues facing the organization. Try to assess upsides and downsides of the possible scenarios.
Use by managers
The basic concepts of the process are relatively simple. In terms of the overall approach to forecasting, they can be divided into three main groups of activities (which are, generally speaking, common to all long range forecasting processes):
Environmental analysis
Scenario planning
Corporate strategy
The first of these groups quite simply comprises the normal environmental analysis. This is almost exactly the same as that which should be undertaken as the first stage of any serious long-range planning. However, the quality of this analysis is especially important in the context of scenario planning.
The central part represents the specific techniques – covered here – which differentiate the scenario forecasting process from the others in long-range planning.
The final group represents all the subsequent processes which go towards producing the corporate strategy and plans. Again, the requirements are slightly different but in general they follow all the rules of sound long-range planning.
Applications
Business
In the past, strategic plans have often considered only the "official future", which was usually a straight-line graph of current trends carried into the future. Often the trend lines were generated by the accounting department, and lacked discussions of demographics, or qualitative differences in social conditions.
These simplistic guesses are surprisingly good most of the time, but fail to consider qualitative social changes that can affect a business or government. Paul J. H. Schoemaker offers a strong managerial case for the use of scenario planning in business and had wide impact.
The approach may have had more impact outside Shell than within, as many others firms and consultancies started to benefit as well from scenario planning. Scenario planning is as much art as science, and prone to a variety of traps (both in process and content) as enumerated by Paul J. H. Schoemaker. More recently scenario planning has been discussed as a tool to improve the strategic agility, by cognitively preparing not only multiple scenarios but also multiple consistent strategies.
Military
Scenario planning is also extremely popular with military planners. Most states' department of war maintains a continuously updated series of strategic plans to cope with well-known military or strategic problems. These plans are almost always based on scenarios, and often the plans and scenarios are kept up-to-date by war games, sometimes played out with real troops. This process was first carried out (arguably the method was invented by) the Prussian general staff of the mid-19th century.
Finance
In economics and finance, a financial institution might use scenario analysis to forecast several possible scenarios for the economy (e.g. rapid growth, moderate growth, slow growth) and for financial returns (for bonds, stocks, cash, etc.) in each of those scenarios. It might consider sub-sets of each of the possibilities. It might further seek to determine correlations and assign probabilities to the scenarios (and sub-sets if any). Then it will be in a position to consider how to distribute assets between asset types (i.e. asset allocation); the institution can also calculate the scenario-weighted expected return (which figure will indicate the overall attractiveness of the financial environment). It may also perform stress testing, using adverse scenarios.
Depending on the complexity of the problem, scenario analysis can be a demanding exercise. It can be difficult to foresee what the future holds (e.g. the actual future outcome may be entirely unexpected), i.e. to foresee what the scenarios are, and to assign probabilities to them; and this is true of the general forecasts never mind the implied financial market returns. The outcomes can be modeled mathematically/statistically e.g. taking account of possible variability within single scenarios as well as possible relationships between scenarios. In general, one should take care when assigning probabilities to different scenarios as this could invite a tendency to consider only the scenario with the highest probability.
Geopolitics
In politics or geopolitics, scenario analysis involves reflecting on the possible alternative paths of a social or political environment and possibly diplomatic and war risks.
History of use by academic and commercial organizations
Most authors attribute the introduction of scenario planning to Herman Kahn through his work for the US Military in the 1950s at the RAND Corporation where he developed a technique of describing the future in stories as if written by people in the future. He adopted the term "scenarios" to describe these stories. In 1961 he founded the Hudson Institute where he expanded his scenario work to social forecasting and public policy. One of his most controversial uses of scenarios was to suggest that a nuclear war could be won. Though Kahn is often cited as the father of scenario planning, at the same time Kahn was developing his methods at RAND, Gaston Berger was developing similar methods at the Centre d’Etudes Prospectives which he founded in France. His method, which he named 'La Prospective', was to develop normative scenarios of the future which were to be used as a guide in formulating public policy. During the mid-1960s various authors from the French and American institutions began to publish scenario planning concepts such as 'La Prospective' by Berger in 1964 and 'The Next Thirty-Three Years' by Kahn and Wiener in 1967. By the 1970s scenario planning was in full swing with a number of institutions now established to provide support to business including the Hudson Foundation, the Stanford Research Institute (now SRI International), and the SEMA Metra Consulting Group in France. Several large companies also began to embrace scenario planning including DHL Express, Dutch Royal Shell and General Electric.
Possibly as a result of these very sophisticated approaches, and of the difficult techniques they employed (which usually demanded the resources of a central planning staff), scenarios earned a reputation for difficulty (and cost) in use. Even so, the theoretical importance of the use of alternative scenarios, to help address the uncertainty implicit in long-range forecasts, was dramatically underlined by the widespread confusion which followed the Oil Shock of 1973. As a result, many of the larger organizations started to use the technique in one form or another. By 1983 Diffenbach reported that 'alternate scenarios' were the third most popular technique for long-range forecasting – used by 68% of the large organizations he surveyed.
Practical development of scenario forecasting, to guide strategy rather than for the more limited academic uses which had previously been the case, was started by Pierre Wack in 1971 at the Royal Dutch Shell group of companies – and it, too, was given impetus by the Oil Shock two years later. Shell has, since that time, led the commercial world in the use of scenarios – and in the development of more practical techniques to support these. Indeed, as – in common with most forms of long-range forecasting – the use of scenarios has (during the depressed trading conditions of the last decade) reduced to only a handful of private-sector organisations, Shell remains almost alone amongst them in keeping the technique at the forefront of forecasting.
There has only been anecdotal evidence offered in support of the value of scenarios, even as aids to forecasting; and most of this has come from one company – Shell. In addition, with so few organisations making consistent use of them – and with the timescales involved reaching into decades – it is unlikely that any definitive supporting evidenced will be forthcoming in the foreseeable future. For the same reasons, though, a lack of such proof applies to almost all long-range planning techniques. In the absence of proof, but taking account of Shell's well documented experiences of using it over several decades (where, in the 1990s, its then CEO ascribed its success to its use of such scenarios), can be significant benefit to be obtained from extending the horizons of managers' long-range forecasting in the way that the use of scenarios uniquely does.
Process
The part of the overall process which is radically different from most other forms of long-range planning is the central section, the actual production of the scenarios. Even this, though, is relatively simple, at its most basic level. As derived from the approach most commonly used by Shell, it follows six steps:
Decide drivers for change/assumptions
Bring drivers together into a viable framework
Produce 7–9 initial mini-scenarios
Reduce to 2–3 scenarios
Draft the scenarios
Identify the issues arising
Step 1 – decide assumptions/drivers for change
The first stage is to examine the results of environmental analysis to determine which are the most important factors that will decide the nature of the future environment within which the organisation operates. These factors are sometimes called 'variables' (because they will vary over the time being investigated, though the terminology may confuse scientists who use it in a more rigorous manner). Users tend to prefer the term 'drivers' (for change), since this terminology is not laden with quasi-scientific connotations and reinforces the participant's commitment to search for those forces which will act to change the future. Whatever the nomenclature, the main requirement is that these will be informed assumptions.
This is partly a process of analysis, needed to recognise what these 'forces' might be. However, it is likely that some work on this element will already have taken place during the preceding environmental analysis. By the time the formal scenario planning stage has been reached, the participants may have already decided – probably in their sub-conscious rather than formally – what the main forces are.
In the ideal approach, the first stage should be to carefully decide the overall assumptions on which the scenarios will be based. Only then, as a second stage, should the various drivers be specifically defined. Participants, though, seem to have problems in separating these stages.
Perhaps the most difficult aspect though, is freeing the participants from the preconceptions they take into the process with them. In particular, most participants will want to look at the medium term, five to ten years ahead rather than the required longer-term, ten or more years ahead. However, a time horizon of anything less than ten years often leads participants to extrapolate from present trends, rather than consider the alternatives which might face them. When, however, they are asked to consider timescales in excess of ten years they almost all seem to accept the logic of the scenario planning process, and no longer fall back on that of extrapolation. There is a similar problem with expanding participants horizons to include the whole external environment.
Brainstorming
In any case, the brainstorming which should then take place, to ensure that the list is complete, may unearth more variables – and, in particular, the combination of factors may suggest yet others.
A very simple technique which is especially useful at this – brainstorming – stage, and in general for handling scenario planning debates is derived from use in Shell where this type of approach is often used. An especially easy approach, it only requires a conference room with a bare wall and copious supplies of 3M Post-It Notes.
The six to ten people ideally taking part in such face-to-face debates should be in a conference room environment which is isolated from outside interruptions. The only special requirement is that the conference room has at least one clear wall on which Post-It notes will stick. At the start of the meeting itself, any topics which have already been identified during the environmental analysis stage are written (preferably with a thick magic marker, so they can be read from a distance) on separate Post-It Notes. These Post-It Notes are then, at least in theory, randomly placed on the wall. In practice, even at this early stage the participants will want to cluster them in groups which seem to make sense. The only requirement (which is why Post-It Notes are ideal for this approach) is that there is no bar to taking them off again and moving them to a new cluster.
A similar technique – using 5" by 3" index cards – has also been described (as the 'Snowball Technique'), by Backoff and Nutt, for grouping and evaluating ideas in general.
As in any form of brainstorming, the initial ideas almost invariably stimulate others. Indeed, everyone should be encouraged to add their own Post-It Notes to those on the wall. However it differs from the 'rigorous' form described in 'creative thinking' texts, in that it is much slower paced and the ideas are discussed immediately. In practice, as many ideas may be removed, as not being relevant, as are added. Even so, it follows many of the same rules as normal brainstorming and typically lasts the same length of time – say, an hour or so only.
It is important that all the participants feel they 'own' the wall – and are encouraged to move the notes around themselves. The result is a very powerful form of creative decision-making for groups, which is applicable to a wide range of situations (but is especially powerful in the context of scenario planning). It also offers a very good introduction for those who are coming to the scenario process for the first time. Since the workings are largely self-evident, participants very quickly come to understand exactly what is involved.
Important and uncertain
This step is, though, also one of selection – since only the most important factors will justify a place in the scenarios. The 80:20 Rule here means that, at the end of the process, management's attention must be focused on a limited number of most important issues. Experience has proved that offering a wider range of topics merely allows them to select those few which interest them, and not necessarily those which are most important to the organisation.
In addition, as scenarios are a technique for presenting alternative futures, the factors to be included must be genuinely 'variable'. They should be subject to significant alternative outcomes. Factors whose outcome is predictable, but important, should be spelled out in the introduction to the scenarios (since they cannot be ignored). The Important Uncertainties Matrix, as reported by Kees van der Heijden of Shell, is a useful check at this stage.
At this point it is also worth pointing out that a great virtue of scenarios is that they can accommodate the input from any other form of forecasting. They may use figures, diagrams or words in any combination. No other form of forecasting offers this flexibility.
Step 2 – bring drivers together into a viable framework
The next step is to link these drivers together to provide a meaningful framework. This may be obvious, where some of the factors are clearly related to each other in one way or another. For instance, a technological factor may lead to market changes, but may be constrained by legislative factors. On the other hand, some of the 'links' (or at least the 'groupings') may need to be artificial at this stage. At a later stage more meaningful links may be found, or the factors may then be rejected from the scenarios. In the most theoretical approaches to the subject, probabilities are attached to the event strings. This is difficult to achieve, however, and generally adds little – except complexity – to the outcomes.
This is probably the most (conceptually) difficult step. It is where managers' 'intuition' – their ability to make sense of complex patterns of 'soft' data which more rigorous analysis would be unable to handle – plays an important role. There are, however, a range of techniques which can help; and again the Post-It-Notes approach is especially useful:
Thus, the participants try to arrange the drivers, which have emerged from the first stage, into groups which seem to make sense to them. Initially there may be many small groups. The intention should, therefore, be to gradually merge these (often having to reform them from new combinations of drivers to make these bigger groups work). The aim of this stage is eventually to make 6–8 larger groupings; 'mini-scenarios'. Here the Post-It Notes may be moved dozens of times over the length – perhaps several hours or more – of each meeting. While this process is taking place the participants will probably want to add new topics – so more Post-It Notes are added to the wall. In the opposite direction, the unimportant ones are removed (possibly to be grouped, again as an 'audit trail' on another wall). More important, the 'certain' topics are also removed from the main area of debate – in this case they must be grouped in clearly labelled area of the main wall.
As the clusters – the 'mini-scenarios' – emerge, the associated notes may be stuck to each other rather than individually to the wall; which makes it easier to move the clusters around (and is a considerable help during the final, demanding stage to reducing the scenarios to two or three).
The great benefit of using Post-It Notes is that there is no bar to participants changing their minds. If they want to rearrange the groups – or simply to go back (iterate) to an earlier stage – then they strip them off and put them in their new position.
Step 3 – produce initial mini-scenarios
The outcome of the previous step is usually between seven and nine logical groupings of drivers. This is usually easy to achieve. The 'natural' reason for this may be that it represents some form of limit as to what participants can visualise.
Having placed the factors in these groups, the next action is to work out, very approximately at this stage, what is the connection between them. What does each group of factors represent?
Step 4 – reduce to two or three scenarios
The main action, at this next stage, is to reduce the seven to nine mini-scenarios/groupings detected at the previous stage to two or three larger scenarios
There is no theoretical reason for reducing to just two or three scenarios, only a practical one. It has been found that the managers who will be asked to use the final scenarios can only cope effectively with a maximum of three versions! Shell started, more than three decades ago, by building half a dozen or more scenarios – but found that the outcome was that their managers selected just one of these to concentrate on. As a result, the planners reduced the number to three, which managers could handle easily but could no longer so easily justify the selection of only one! This is the number now recommended most frequently in most of the literature.
Complementary scenarios
As used by Shell, and as favoured by a number of the academics, two scenarios should be complementary; the reason being that this helps avoid managers 'choosing' just one, 'preferred', scenario – and lapsing once more into single-track forecasting (negating the benefits of using 'alternative' scenarios to allow for alternative, uncertain futures). This is, however, a potentially difficult concept to grasp, where managers are used to looking for opposites; a good and a bad scenario, say, or an optimistic one versus a pessimistic one – and indeed this is the approach (for small businesses) advocated by Foster. In the Shell approach, the two scenarios are required to be equally likely, and between them to cover all the 'event strings'/drivers. Ideally they should not be obvious opposites, which might once again bias their acceptance by users, so the choice of 'neutral' titles is important. For example, Shell's two scenarios at the beginning of the 1990s were titled 'Sustainable World' and 'Global Mercantilism'[xv]. In practice, we found that this requirement, much to our surprise, posed few problems for the great majority, 85%, of those in the survey; who easily produced 'balanced' scenarios. The remaining 15% mainly fell into the expected trap of 'good versus bad'. We have found that our own relatively complex (OBS) scenarios can also be made complementary to each other; without any great effort needed from the teams involved; and the resulting two scenarios are both developed further by all involved, without unnecessary focusing on one or the other.
Testing
Having grouped the factors into these two scenarios, the next step is to test them, again, for viability. Do they make sense to the participants? This may be in terms of logical analysis, but it may also be in terms of intuitive 'gut-feel'. Once more, intuition often may offer a useful – if academically less respectable – vehicle for reacting to the complex and ill-defined issues typically involved. If the scenarios do not intuitively 'hang together', why not? The usual problem is that one or more of the assumptions turns out to be unrealistic in terms of how the participants see their world. If this is the case then you need to return to the first step – the whole scenario planning process is above all an iterative one (returning to its beginnings a number of times until the final outcome makes the best sense).
Step 5 – write the scenarios
The scenarios are then 'written up' in the most suitable form. The flexibility of this step often confuses participants, for they are used to forecasting processes which have a fixed format. The rule, though, is that you should produce the scenarios in the form most suitable for use by the managers who are going to base their strategy on them. Less obviously, the managers who are going to implement this strategy should also be taken into account. They will also be exposed to the scenarios, and will need to believe in these. This is essentially a 'marketing' decision, since it will be very necessary to 'sell' the final results to the users. On the other hand, a not inconsiderable consideration may be to use the form the author also finds most comfortable. If the form is alien to him or her the chances are that the resulting scenarios will carry little conviction when it comes to the 'sale'.
Most scenarios will, perhaps, be written in word form (almost as a series of alternative essays about the future); especially where they will almost inevitably be qualitative which is hardly surprising where managers, and their audience, will probably use this in their day to day communications. Some, though use an expanded series of lists and some enliven their reports by adding some fictional 'character' to the material – perhaps taking literally the idea that they are stories about the future – though they are still clearly intended to be factual. On the other hand, they may include numeric data and/or diagrams – as those of Shell do (and in the process gain by the acid test of more measurable 'predictions').
Step 6 – identify issues arising
The final stage of the process is to examine these scenarios to determine what are the most critical outcomes; the 'branching points' relating to the 'issues' which will have the greatest impact (potentially generating 'crises') on the future of the organisation. The subsequent strategy will have to address these – since the normal approach to strategy deriving from scenarios is one which aims to minimise risk by being 'robust' (that is it will safely cope with all the alternative outcomes of these 'life and death' issues) rather than aiming for performance (profit) maximisation by gambling on one outcome.
Use of scenarios
Scenarios may be used in a number of ways:
a) Containers for the drivers/event strings
Most basically, they are a logical device, an artificial framework, for presenting the individual factors/topics (or coherent groups of these) so that these are made easily available for managers' use – as useful ideas about future developments in their own right – without reference to the rest of the scenario. It should be stressed that no factors should be dropped, or even given lower priority, as a result of producing the scenarios. In this context, which scenario contains which topic (driver), or issue about the future, is irrelevant.
b) Tests for consistency
At every stage it is necessary to iterate, to check that the contents are viable and make any necessary changes to ensure that they are; here the main test is to see if the scenarios seem to be internally consistent – if they are not then the writer must loop back to earlier stages to correct the problem. Though it has been mentioned previously, it is important to stress once again that scenario building is ideally an iterative process. It usually does not just happen in one meeting – though even one attempt is better than none – but takes place over a number of meetings as the participants gradually refine their ideas.
c) Positive perspectives
Perhaps the main benefit deriving from scenarios, however, comes from the alternative 'flavors' of the future their different perspectives offer. It is a common experience, when the scenarios finally emerge, for the participants to be startled by the insight they offer – as to what the general shape of the future might be – at this stage it no longer is a theoretical exercise but becomes a genuine framework (or rather set of alternative frameworks) for dealing with that.
Scenario planning compared to other techniques
Scenario planning differs from contingency planning, sensitivity analysis and computer simulations.
Contingency planning is a "What if" tool, that only takes into account one uncertainty. However, scenario planning considers combinations of uncertainties in each scenario. Planners also try to select especially plausible but uncomfortable combinations of social developments.
Sensitivity analysis analyzes changes in one variable only, which is useful for simple changes, while scenario planning tries to expose policy makers to significant interactions of major variables.
While scenario planning can benefit from computer simulations, scenario planning is less formalized, and can be used to make plans for qualitative patterns that show up in a wide variety of simulated events.
During the past 5 years, computer supported Morphological Analysis has been employed as aid in scenario development by the Swedish Defence Research Agency in Stockholm. This method makes it possible to create a multi-variable morphological field which can be treated as an inference model – thus integrating scenario planning techniques with contingency analysis and sensitivity analysis.
Scenario analysis
Scenario analysis is a process of analyzing future events by considering alternative possible outcomes (sometimes called "alternative worlds"). Thus, scenario analysis, which is one of the main forms of projection, does not try to show one exact picture of the future. Instead, it presents several alternative future developments. Consequently, a scope of possible future outcomes is observable. Not only are the outcomes observable, also the development paths leading to the outcomes. In contrast to prognoses, the scenario analysis is not based on extrapolation of the past or the extension of past trends. It does not rely on historical data and does not expect past observations to remain valid in the future. Instead, it tries to consider possible developments and turning points, which may only be connected to the past. In short, several scenarios are fleshed out in a scenario analysis to show possible future outcomes. Each scenario normally combines optimistic, pessimistic, and more and less probable developments. However, all aspects of scenarios should be plausible. Although highly discussed, experience has shown that around three scenarios are most appropriate for further discussion and selection. More scenarios risks making the analysis overly complicated. Scenarios are often confused with other tools and approaches to planning.
Principle
Scenario-building is designed to allow improved decision-making by allowing deep consideration of outcomes and their implications.
A scenario is a tool used during requirements analysis to describe a specific use of a proposed system. Scenarios capture the system, as viewed from the outside
Scenario analysis can also be used to illuminate "wild cards." For example, analysis of the possibility of the earth being struck by a meteor suggests that whilst the probability is low, the damage inflicted is so high that the event is much more important (threatening) than the low probability (in any one year) alone would suggest. However, this possibility is usually disregarded by organizations using scenario analysis to develop a strategic plan since it has such overarching repercussions.
Combination of Delphi and scenarios
Scenario planning concerns planning based on the systematic examination of the future by picturing plausible and consistent images of that future. The Delphi method attempts to develop systematically expert opinion consensus concerning future developments and events. It is a judgmental forecasting procedure in the form of an anonymous, written, multi-stage survey process, where feedback of group opinion is provided after each round.
Numerous researchers have stressed that both approaches are best suited to be combined. Due to their process similarity, the two methodologies can be easily combined. The output of the different phases of the Delphi method can be used as input for the scenario method and vice versa. A combination makes a realization of the benefits of both tools possible. In practice, usually one of the two tools is considered the dominant methodology and the other one is added on at some stage.
The variant that is most often found in practice is the integration of the Delphi method into the scenario process (see e.g. Rikkonen, 2005; von der Gracht, 2008;). Authors refer to this type as Delphi-scenario (writing), expert-based scenarios, or Delphi panel derived scenarios. Von der Gracht (2010) is a scientifically valid example of this method. Since scenario planning is “information hungry”, Delphi research can deliver valuable input for the process. There are various types of information output of Delphi that can be used as input for scenario planning. Researchers can, for example, identify relevant events or developments and, based on expert opinion, assign probabilities to them. Moreover, expert comments and arguments provide deeper insights into relationships of factors that can, in turn, be integrated into scenarios afterwards. Also, Delphi helps to identify extreme opinions and dissent among the experts. Such controversial topics are particularly suited for extreme scenarios or wildcards.
In his doctoral thesis, Rikkonen (2005) examined the utilization of Delphi techniques in scenario planning and, concretely, in construction of scenarios. The author comes to the conclusion that the Delphi technique has instrumental value in providing different alternative futures and the argumentation of scenarios. It is therefore recommended to use Delphi in order to make the scenarios more profound and to create confidence in scenario planning. Further benefits lie in the simplification of the scenario writing process and the deep understanding of the interrelations between the forecast items and social factors.
Critique
While there is utility in weighting hypotheses and branching potential outcomes from them, reliance on scenario analysis without reporting some parameters of measurement accuracy (standard errors, confidence intervals of estimates, metadata, standardization and coding, weighting for non-response, error in reportage, sample design, case counts, etc.) is a poor second to traditional prediction. Especially in “complex” problems, factors and assumptions do not correlate in lockstep fashion. Once a specific sensitivity is undefined, it may call the entire study into question.
It is faulty logic to think, when arbitrating results, that a better hypothesis will render empiricism unnecessary. In this respect, scenario analysis tries to defer statistical laws (e.g., Chebyshev's inequality Law), because the decision rules occur outside a constrained setting. Outcomes are not permitted to “just happen”; rather, they are forced to conform to arbitrary hypotheses ex post, and therefore there is no footing on which to place expected values. In truth, there are no ex ante expected values, only hypotheses, and one is left wondering about the roles of modeling and data decision. In short, comparisons of "scenarios" with outcomes are biased by not deferring to the data; this may be convenient, but it is indefensible.
“Scenario analysis” is no substitute for complete and factual exposure of survey error in economic studies. In traditional prediction, given the data used to model the problem, with a reasoned specification and technique, an analyst can state, within a certain percentage of statistical error, the likelihood of a coefficient being within a certain numerical bound. This exactitude need not come at the expense of very disaggregated statements of hypotheses. R Software, specifically the module “WhatIf,” (in the context, see also Matchit and Zelig) has been developed for causal inference, and to evaluate counterfactuals. These programs have fairly sophisticated treatments for determining model dependence, in order to state with precision how sensitive the results are to models not based on empirical evidence.
Another challenge of scenario-building is that "predictors are part of the social context about which they are trying to make a prediction and may influence that context in the process". As a consequence, societal predictions can become self-destructing. For example, a scenario in which a large percentage of a population will become HIV infected based on existing trends may cause more people to avoid risky behavior and thus reduce the HIV infection rate, invalidating the forecast (which might have remained correct if it had not been publicly known). Or, a prediction that cybersecurity will become a major issue may cause organizations to implement more secure cybersecurity measures, thus limiting the issue.
Critique of Shell's use of scenario planning
In the 1970s, many energy companies were surprised by both environmentalism and the OPEC cartel, and thereby lost billions of dollars of revenue by mis-investment. The dramatic financial effects of these changes led at least one organization, Royal Dutch Shell, to implement scenario planning. The analysts of this company publicly estimated that this planning process made their company the largest in the world. However other observers of Shell's use of scenario planning have suggested that few if any significant long-term business advantages accrued to Shell from the use of scenario methodology. Whilst the intellectual robustness of Shell's long term scenarios was seldom in doubt their actual practical use was seen as being minimal by many senior Shell executives. A Shell insider has commented "The scenario team were bright and their work was of a very high intellectual level. However neither the high level "Group scenarios" nor the country level scenarios produced with operating companies really made much difference when key decisions were being taken".
The use of scenarios was audited by Arie de Geus's team in the early 1980s and they found that the decision-making processes following the scenarios were the primary cause of the lack of strategic implementation ), rather than the scenarios themselves. Many practitioners today spend as much time on the decision-making process as on creating the scenarios themselves.
See also
Decentralized planning (economics)
Hoshin Kanri#Hoshin planning
Futures studies
Futures techniques
Global Scenario Group
Jim Dator (Hawaii Research Center for Futures Studies)
Resilience (organizational)
Robust decision-making
Scenario (computing)
Similar terminology
Feedback loop
System dynamics (also known as Stock and flow)
System thinking
Analogous concepts
Delphi method, including Real-time Delphi
Game theory
Horizon scanning
Morphological analysis
Rational choice theory
Stress testing
Twelve leverage points
Examples
Climate change mitigation scenarios – possible futures in which global warming is reduced by deliberate actions
Dynamic Analysis and Replanning Tool
Energy modeling – the process of building computer models of energy systems
Pentagon Papers
References
Additional Bibliography
D. Erasmus, The future of ICT in financial services: The Rabobank ICT scenarios (2008).
M. Godet, Scenarios and Strategic Management, Butterworths (1987).
M. Godet, From Anticipation to Action: A Handbook of Strategic Prospective. Paris: Unesco, (1993).
Adam Kahane, Solving Tough Problems: An Open Way of Talking, Listening, and Creating New Realities (2007)
H. Kahn, The Year 2000, Calman-Levy (1967).
Herbert Meyer, "Real World Intelligence", Weidenfeld & Nicolson, 1987,
National Intelligence Council (NIC) , "Mapping the Global Future", 2005,
M. Lindgren & H. Bandhold, Scenario planning – the link between future and strategy, Palgrave Macmillan, 2003
G. Wright& G. Cairns, Scenario thinking: practical approaches to the future, Palgrave Macmillan, 2011
A. Schuehly, F. Becker t& F. Klein, Real Time Strategy: When Strategic Foresight Meets Artificial Intelligence, Emerald, 2020*
A. Ruser, Sociological Quasi-Labs: The Case for Deductive Scenario Development, Current Sociology Vol63(2): 170-181, https://journals.sagepub.com/doi/pdf/10.1177/0011392114556581
Scientific journals
Foresight
Futures
Futures & Foresight Science
Journal of Futures Studies
Technological Forecasting and Social Change
External links
Wikifutures wiki; Scenario page—wiki also includes several scenarios (GFDL licensed)
ScenarioThinking.org —more than 100 scenarios developed on various global issues, on a wiki for public use
Shell Scenarios Resources—Resources on what scenarios are, Shell's new and old scenario's, explorer's guide and other scenario resources
Learn how to use Scenario Manager in Excel to do Scenario Analysis
Systems Innovation (SI) courseware
Further reading
"Learning from the Future: Competitive Foresight Scenarios", Liam Fahey and Robert M. Randall, Published by John Wiley and Sons, 1997, , Google book
"Shirt-sleeve approach to long-range plans.", Linneman, Robert E, Kennell, John D.; Harvard Business Review; Mar/Apr77, Vol. 55 Issue 2, p141
Business models
Futures techniques
Military strategy
Risk analysis
Risk management
Strategic management
Systems thinking
Systems engineering
Types of marketing | Scenario planning | [
"Engineering"
] | 9,449 | [
"Systems engineering"
] |
600,570 | https://en.wikipedia.org/wiki/H-space | In mathematics, an H-space is a homotopy-theoretic version of a generalization of the notion of topological group, in which the axioms on associativity and inverses are removed.
Definition
An H-space consists of a topological space , together with an element of and a continuous map , such that and the maps and are both homotopic to the identity map through maps sending to . This may be thought of as a pointed topological space together with a continuous multiplication for which the basepoint is an identity element up to basepoint-preserving homotopy.
One says that a topological space is an H-space if there exists and such that the triple is an H-space as in the above definition. Alternatively, an H-space may be defined without requiring homotopies to fix the basepoint , or by requiring to be an exact identity, without any consideration of homotopy. In the case of a CW complex, all three of these definitions are in fact equivalent.
Examples and properties
The standard definition of the fundamental group, together with the fact that it is a group, can be rephrased as saying that the loop space of a pointed topological space has the structure of an H-group, as equipped with the standard operations of concatenation and inversion. Furthermore a continuous basepoint preserving map of pointed topological space induces a H-homomorphism of the corresponding loop spaces; this reflects the group homomorphism on fundamental groups induced by a continuous map.
It is straightforward to verify that, given a pointed homotopy equivalence from a H-space to a pointed topological space, there is a natural H-space structure on the latter space. As such, the existence of an H-space structure on a given space is only dependent on pointed homotopy type.
The multiplicative structure of an H-space adds structure to its homology and cohomology groups. For example, the cohomology ring of a path-connected H-space with finitely generated and free cohomology groups is a Hopf algebra. Also, one can define the Pontryagin product on the homology groups of an H-space.
The fundamental group of an H-space is abelian. To see this, let X be an H-space with identity e and let f and g be loops at e. Define a map F: [0,1] × [0,1] → X by F(a,b) = f(a)g(b). Then F(a,0) = F(a,1) = f(a)e is homotopic to f, and F(0,b) = F(1,b) = eg(b) is homotopic to g. It is clear how to define a homotopy from [f][g] to [g][f].
Adams' Hopf invariant one theorem, named after Frank Adams, states that S0, S1, S3, S7 are the only spheres that are H-spaces. Each of these spaces forms an H-space by viewing it as the subset of norm-one elements of the reals, complexes, quaternions, and octonions, respectively, and using the multiplication operations from these algebras. In fact, S0, S1, and S3 are groups (Lie groups) with these multiplications. But S7 is not a group in this way because octonion multiplication is not associative, nor can it be given any other continuous multiplication for which it is a group.
See also
Topological group
Čech cohomology
Hopf algebra
Topological monoid
H-object
Notes
References
. Section 3.C
.
.
Homotopy theory
Algebraic topology
Hopf algebras | H-space | [
"Mathematics"
] | 776 | [
"Fields of abstract algebra",
"Topology",
"Algebraic topology"
] |
600,618 | https://en.wikipedia.org/wiki/Duality%20%28order%20theory%29 | In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P. It is easy to see that this construction, which can be depicted by flipping the Hasse diagram for P upside down, will indeed yield a partially ordered set. In a broader sense, two partially ordered sets are also said to be duals if they are dually isomorphic, i.e. if one poset is order isomorphic to the dual of the other.
The importance of this simple definition stems from the fact that every definition and theorem of order theory can readily be transferred to the dual order. Formally, this is captured by the Duality Principle for ordered sets:
If a given statement is valid for all partially ordered sets, then its dual statement, obtained by inverting the direction of all order relations and by dualizing all order theoretic definitions involved, is also valid for all partially ordered sets.
If a statement or definition is equivalent to its dual then it is said to be self-dual. Note that the consideration of dual orders is so fundamental that it often occurs implicitly when writing ≥ for the dual order of ≤ without giving any prior definition of this "new" symbol.
Examples
Naturally, there are a great number of examples for concepts that are dual:
Greatest elements and least elements
Maximal elements and minimal elements
Least upper bounds (suprema, ∨) and greatest lower bounds (infima, ∧)
Upper sets and lower sets
Ideals and filters
Closure operators and kernel operators.
Examples of notions which are self-dual include:
Being a (complete) lattice
Monotonicity of functions
Distributivity of lattices, i.e. the lattices for which ∀x,y,z: x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z) holds are exactly those for which the dual statement ∀x,y,z: x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z) holds
Being a Boolean algebra
Being an order isomorphism.
Since partial orders are antisymmetric, the only ones that are self-dual are the equivalence relations (but the notion of partial order is self-dual).
See also
Converse relation
List of Boolean algebra topics
Transpose graph
Duality in category theory, of which duality in order theory is a special case
References
Order theory
Order theory | Duality (order theory) | [
"Mathematics"
] | 538 | [
"Mathematical structures",
"Category theory",
"Duality theories",
"Geometry",
"Order theory"
] |
600,624 | https://en.wikipedia.org/wiki/Animals%20in%20space | Animals in space originally served to test the survivability of spaceflight, before human spaceflights were attempted. Later, many species were flown to investigate various biological processes and the effects microgravity and space flight might have on them. Bioastronautics is an area of bioengineering research that spans the study and support of life in space. To date, seven national space programs have flown non-human animals into space: the United States, Soviet Union, France, Argentina, China, Japan and Iran.
A wide variety of non-human animals have been launched into space, including monkeys and apes, dogs, cats, tortoises, mice, rats, rabbits, fish, frogs, spiders, insects, and quail eggs (which hatched on Mir in 1990). The US launched the first Earthlings into space, with fruit flies surviving a 1947 flight, followed by primates in 1949. The Soviet space program launched multiple dogs into space, with the first sub-orbital flights in 1951, and first orbital flights in 1957.
Two tortoises and several varieties of plants were the first Earthlings to circle the Moon in September 1968 on the Zond 5 mission. In 1972, five mice nicknamed Fe, Fi, Fo, Fum, and Phooey orbited the Moon a record 75 times aboard command module America as part of the Apollo 17 mission (the most recent to put Earthlings into lunar orbit).
Background
Animals had been used in aeronautic exploration since 1783 when the Montgolfier brothers sent a sheep, a duck, and a rooster aloft in a hot air balloon to see if ground-dwelling animals can survive (the duck serving as the experimental control). The limited supply of captured German V-2 rockets led to the U.S. use of high-altitude balloon launches carrying fruit flies, mice, hamsters, guinea pigs, cats, dogs, frogs, goldfish and monkeys to heights of up to . These high-altitude balloon flights from 1947 to 1960 tested radiation exposure, physiological response, life support and recovery systems. The U.S. high-altitude manned balloon flights occurred in the same time frame, one of which also carried fruit flies.
Timeline
1940s
The first animals sent into space were fruit flies aboard a U.S.-launched V-2 rocket on 20 February 1947 from White Sands Missile Range, New Mexico. The purpose of the experiment was to explore the effects of radiation exposure at high altitudes. The rocket reached in 3 minutes 10 seconds, past both the U.S. Air Force and the international 100 km definitions of the boundary of space. The Blossom capsule was ejected and successfully deployed its parachute. The fruit flies were recovered alive. Other V-2 missions carried biological samples, including moss.
Albert II, a rhesus monkey, became the first monkey, first primate, and first mammal in space on 14 June 1949, in a U.S.-launched V-2, after the failure of the original Albert's mission on ascent. Albert I reached only altitude; Albert II reached about , and died on impact after a parachute failure.
Numerous monkeys of several species were flown by the U.S. in the 1950s and 1960s. Monkeys were implanted with sensors to measure vital signs, and many were under anesthesia during launch. The death rate among these monkeys was very high: about two-thirds of all monkeys launched in the 1940s and 1950s died on missions or soon after landing.
1950s
On 31 August 1950, the U.S. launched a mouse into space (137 km) aboard a V-2 (the Albert V flight, which, unlike the Albert I-IV flights, did not have a monkey), however the animal died following descent because the parachute system failed. The U.S. launched several other mice in the 1950s.
On 22 July 1951, the Soviet Union launched the R-1 IIIA-1 flight, carrying the dogs Tsygan (, "Gypsy" or "Țigan/Țagaur" in romani language) and Dezik () into space, but not into orbit. These two dogs were the first living higher organisms successfully recovered from a spaceflight. Both space dogs survived the flight, although Dezik would die on a subsequent flight. The U.S. launched mice aboard spacecraft later that year; however, they failed to reach the altitude for true spaceflight.
On 3 November 1957, the second-ever orbiting spacecraft carried the first animal into orbit, the dog Laika, launched aboard the Soviet Sputnik 2 spacecraft (nicknamed 'Muttnik' in the West). Laika died during the flight, as was expected because the technology to return spacecraft from orbit had not yet been developed. At least 10 other dogs were launched into orbit and numerous others on sub-orbital flights before the historic date of 12 April 1961, when Yuri Gagarin became the first human in space.
On 13 December 1958, a Jupiter IRBM, AM-13, was launched from Cape Canaveral, Florida, with a United States Navy-trained South American squirrel monkey named Gordo on board. The nose cone recovery parachute failed to operate and Gordo was lost. Telemetry data sent back during the flight showed that the monkey survived the 10 g of launch, 8 minutes of weightlessness and 40 g of reentry at . The nose cone sank downrange from Cape Canaveral and was not recovered.
Monkeys Miss Able and Miss Baker became the first monkeys to survive spaceflight after their 1959 flight. On 28 May 1959, aboard Jupiter IRBM AM-18, were a American-born rhesus monkey, Able, from Independence, Kansas, and a squirrel monkey from Peru, Baker. The monkeys rode in the nose cone of the missile to an altitude of and a distance of down the Atlantic Missile Range from Cape Canaveral, Florida. They withstood forces 38 times the normal pull of gravity and were weightless for about 9 minutes. A top speed of was reached during their 16-minute flight. The monkeys survived the flight in good condition. Able died four days after the flight from a reaction to anesthesia, while undergoing surgery to remove an infected medical electrode. Baker was the center of media attention for the next several months as she was watched closely for any ill-effects from her space flight. She was even mated in an attempt to test her reproductive system. Baker lived until 29 November 1984, at the U.S. Space and Rocket Center in Huntsville, Alabama.
On 2 July 1959, a launch of a Soviet R2 rocket, which reached , carried two space dogs and Marfusha, the first rabbit to go into space.
A 19 September 1959 launch, a Jupiter AM-23, carried two frogs and 12 mice but was destroyed during launch.
On 4 December 1959, a rhesus macaque Sam flew on the Little Joe 2 mission of Project Mercury to an altitude of .
1960s
On 19 August 1960 the Soviet Union launched Sputnik 5 (also known as Korabl-Sputnik 2) which carried the dogs Belka and Strelka, along with a gray rabbit, 40 mice, 2 rats, and 15 flasks of fruit flies and plants. It was the first spacecraft to carry animals into orbit and return them alive. One of Strelka's pups, Pushinka, bred and born after her mission, was given as a present to Caroline Kennedy by Nikita Khrushchev in 1961, and many descendants are known to exist.
The US sent three black mice: Sally, Amy and Moe 1,000 km up and 8,000 km distance from Cape Canaveral on 13 October 1960 using an Atlas D 71D launch vehicle. The mice were retrieved from the nosecone near Ascension Island and were said to be in good condition.
On 31 January 1961, Ham, a chimpanzee, was launched into sub-orbital space in a Mercury capsule aboard a Redstone rocket to become the first great ape in space. Ham's mission was Mercury-Redstone 2. The chimpanzee had been trained to pull levers to receive rewards of banana pellets and avoid electric shocks. His flight demonstrated the ability to perform tasks during spaceflight. A little over three months later the United States sent Alan Shepard into space on a suborbital flight.
Enos became the first and only chimpanzee to reach Earth orbit when, on 29 November 1961, he flew two orbits in a Mercury capsule on the Mercury-Atlas 5 mission. Two months later Project Mercury pilot John Glenn orbited the Earth.
On 9 March 1961 the Soviet Union launched the Korabl-Sputnik 4 that carried a dog named Chernushka, some mice, frogs and, for the first time into space, a guinea pig. All were successfully recovered.
France flew their first rat (Hector) into space on 22 February 1961. Two more rats were flown in October 1962.
On 18 October 1963, France launched Félicette the cat aboard Veronique AGI sounding rocket No. 47. The launch was directed by the French Centre d'Enseignement et de Recherches de Médecine Aéronautique (CERMA). Félicette was recovered alive after a 15-minute flight and a descent by parachute. Félicette had electrodes implanted into her brain, and the recorded neural impulses were transmitted back to Earth. After two months of analysis, she was euthanized so an autopsy could be performed. On 18 December 2019 a bronze statue with the effigy of Félicette was inaugurated at the "Université internationalle de l'espace" in Strasbourg, France. A second cat was sent to space by CERMA on 24 October 1963, but the flight ran into difficulties that prevented recovery. In 1967, France launched two pig-tailed macaque monkeys into suborbital space.
China launched mice and rats in 1964 and 1965, and two dogs in 1966.
During the Voskhod program, two Soviet space dogs, Veterok (Ветерок, Little Wind) and Ugolyok (Уголёк, Blackie), were launched on 22 February 1966, on board Cosmos 110 and spent 22 days in orbit before landing on 16 March. This spaceflight of record-breaking duration was not surpassed by humans until Soyuz 11 in 1971 and still stands as the longest space flight by dogs.
The US launched Biosatellite I in 1966 and Biosatellite I/II in 1967 with fruit flies, parasitic wasps, flour beetles and frog eggs, along with bacteria, amoebae, plants and fungi.
On 11 April 1967, Argentina also launched the rat Belisario, atop a Yarará rocket, from Cordoba military range, which was recovered successfully. This flight was followed by a series of subsequent flights using rats. It is unclear if any Argentinean biological flights passed the 100 km limit of space.
The first animals in deep space, the first to circle the Moon, and the first two tortoises in space were launched on Zond 5 on 14 September 1968 by the Soviet Union. The Horsfield's tortoises were sent on a circumlunar voyage to the Moon along with wine flies, meal worms, and other biological specimens. These were the first inhabitants of Earth to travel around the Moon. The capsule overshot its terrestrial landing site but was successfully recovered at sea on 21 September. The animals survived but had some weight loss. More turtles followed on the circumlunar Zond 6 mission of November 1968 (ahead of the December U.S. crewed Apollo 8 mission) and four turtles flew on the circumlunar Zond 7 mission which flew around the Moon on August 11, 1969, three weeks after Apollo 11's Moon walk.
On 28 June 1969, the US launched the monkey Bonny, a macaque, on Biosatellite 3 in what was intended to have been a 30-day orbit around the Earth, with the monkey being fed by food pellets from a dispenser that he had been trained to operate. Bonny's health deteriorated rapidly and he was returned to Earth on 7 July, but died the next day after the Biosatellite capsule was recovered in the Pacific Ocean.
In total in the 1950s and 1960s, the Soviet Union launched missions with at least 57 passenger slots for dogs. The actual number of dogs in space is smaller, because some dogs flew more than once.
On 23 December 1969, as part of the 'Operación Navidad' (Operation Christmas), Argentina launched Juan (a cai monkey, native of Argentina's Misiones Province) using a Canopus II rocket. It ascended 82 kilometers and then was recovered successfully. Later, on 1 February 1970 the experience was repeated with a female monkey of the same species using a X-1 Panther rocket. It reached a higher altitude than its predecessor, but it was lost after the capsule's parachute failed.
1970s
Two bullfrogs were launched on a one-way mission on the Orbiting Frog Otolith satellite on 9 November 1970, to understand more about space motion sickness.
Apollo 16, launched on 16 April 1972, carried nematodes. Apollo 17, launched on 7 December 1972, carried five pocket mice, Fe, Fi, Fo, Fum, and Phooey, who stayed in the command module with astronaut Ronald Evans as it circled the Moon for six days. One of the mice died on the trip.
Skylab 3 (1973) carried pocket mice and the first fish in space (a mummichog), and the first spiders in space (garden spiders named Arabella and Anita). Mummichog were also flown by the U.S. on the Apollo–Soyuz joint mission, launched 15 July 1975.
The Soviets flew several Bion program missions which consisted of satellites with biological cargoes. On these launches they flew tortoises, rats, and mummichog. On Soyuz 20, launched 17 November 1975, tortoises set the duration record for an animal in space when they spent 90.5 days in space. Salyut 5 on 22 June 1976, carried tortoises and a fish (a zebra danio).
1980s
The Soviet Union sent eight monkeys into space in the 1980s on Bion flights. Bion flights also flew zebra danio, fruit flies, rats, stick insect eggs and the first newts in space.
In 1985, the U.S. sent two squirrel monkeys aboard Spacelab 3 on the Space Shuttle with 24 male albino rats and stick insect eggs.
Bion 7 (1985) had 10 newts (Pleurodeles waltl) on board. The newts had part of their front limbs amputated, to study the rate of regeneration in space, knowledge to understand human recovery from space injuries.
After an experiment was lost in the Space Shuttle Challenger disaster, chicken embryos (fertilized eggs) were sent into space in an experiment on STS-29 in 1989. The experiment was designed for a student contest.
1990s
Four monkeys flew aboard the last Bion flights of the Soviet Union as well as frogs and fruit flies. The Foton program flights carried dormant brine shrimp (Artemia franciscana), newts, fruit flies, and sand desert beetles (Trigonoscelis gigas).
China launched guinea pigs in 1990.
Toyohiro Akiyama, a Japanese journalist, carried Japanese tree frogs with him during his trip to the Mir space station in December 1990. Other biological experiments aboard Mir involved quail eggs.
In 1994, four Japanese rice fish successfully mated and laid eggs that hatched to produce healthy fry aboard STS-65, making them the first animals to conceive and bear offspring in space.
Japan launched its first animals, a species of newt, into space on 18 March 1995 aboard the Space Flyer Unit.
During the 1990s the U.S. carried crickets, mice, rats, frogs, newts, fruit flies, snails, carp, medaka (rice fish), oyster toadfish, sea urchins, swordtail fish, spongy moth eggs, stick insect eggs, brine shrimp (Artemia salina), quail eggs, and jellyfish aboard Space Shuttles.
2000s
The last flight of Columbia in 2003 carried silkworms, garden orb spiders, carpenter bees, harvester ants, and Japanese killifish (medaka). Nematodes (C. elegans) from one experiment were found still alive in the debris after the Space Shuttle Columbia disaster.
C. elegans are also part of experiments aboard the International Space Station as well as research using quail eggs.
Earlier Space Shuttle missions included grade school, junior high and high school projects; some of these included ants, stick insect eggs and brine shrimp cysts. Other science missions included spongy moth eggs.
On 12 July 2006, Bigelow Aerospace launched their Genesis I inflatable space module, containing many small items such as toys and simple experiments chosen by company employees that would be observed via camera. These items included insects, perhaps making it the first private flight to launch animals into space. Included were Madagascar hissing cockroaches and Mexican jumping beans — seeds containing live larvae of the moth Cydia saltitans. On 28 June 2007, Bigelow launched Genesis II, a near-twin to Genesis I. This spacecraft also carried Madagascar hissing cockroaches and added South African flat rock scorpions (Hadogenes troglodytes) and seed-harvester ants (Pogonomyrmex californicus).
In September 2007, during the European Space Agency's FOTON-M3 mission, tardigrades, also known as water-bears, were able to survive 10 days of exposure to open-space with only their natural protection.
On the same mission, a number of cockroaches were carried inside a sealed container and at least one of the females, named Nadezhda, conceived during the mission and produced 33 offspring after returning to Earth.
On 15 March 2009, during the countdown of the STS-119, a free-tailed bat was seen clinging to the fuel tank. NASA observers believed the bat would fly off once the Shuttle started to launch, but it did not. Upon analyzing the images, a wildlife expert who provided support to the center said it likely had a broken left wing and some problem with its right shoulder or wrist. The animal most likely perished quickly during Discoverys climb into orbit.
In November 2009, STS-129 took painted lady and monarch butterfly larvae into space for a school experiment as well as thousands of C. elegans roundworms for long-term weight loss studies.
2010s
In May 2011, the last flight of (STS-134) carried two golden orb spiders, named Gladys and Esmeralda, as well as a fruit fly colony as their food source in order to study the effects of microgravity on spiders' behavior. Tardigrades and extremophiles were also sent into orbit.
In November 2011, the Living Interplanetary Flight Experiment on the Fobos-Grunt mission planned to carry tardigrades to Mars and back; however, the mission failed to leave Earth orbit.
In October 2012, 32 medaka fish were delivered to the International Space Station by Soyuz TMA-06M for the new Aquatic Habitat in the Kibo module.
On 28 January 2013, Iranian news agencies reported that Iran sent a monkey in a "Pishgam" rocket to a height of and retrieved a "shipment". Later Iran's space research website uploaded an 18-minute video. The video was uploaded later on YouTube.
On 3 February 2013, on the 31st anniversary of its revolution, Iran became the latest country to launch animals into space. The animals (a mouse, two turtles and some worms) were launched on top of the Kavoshgar 3 rocket and returned alive to Earth.
In January 2014, the search strategies of pavement ants were studied on the ISS.
On 19 July 2014, Russia announced that they launched their Foton-M4 satellite into low Earth orbit (575 kilometers) with one male and four female geckos (possibly gold dust day geckos) as the payload. This was an effort to study the effects of microgravity on reproductive habits of reptiles. On 24 July 2014, it was announced that Russia had lost control of the Foton-M4 satellite, leaving only two months to restore contact before the geckos' food supply was exhausted. Control of the satellite was subsequently restored on 28 July 2014. On 1 September 2014 Russia confirmed the death of all five geckos, stating that their mummified bodies seem to indicate they froze to death. Russia is said to have appointed an emergency commission to investigate the animals' deaths.
On 23 September 2014, SpaceX CRS-4 mission delivered 20 mice to live on the ISS for study of the long-term effects of microgravity on the rodents. This was the first use of the Rodent Research Hardware System.
On 14 April 2015, the SpaceX CRS-6 delivered 20 C57BL/6NTAC mice to live on the ISS for evaluating microgravity as the extreme opposite of a healthy active lifestyle. In the absence of gravity, astronauts are subject to a decrease in muscle, bone, and tendon mass. "Although, we're not out to treat couch potatoes," states head Novartis Institute for Biomedical Research (NIBR) scientist on the project Dr. Sam Cadena, "we're hoping that these experiments will help us to better understand muscle loss in populations where physical activity in any form is not an option; e.g., in the frail elderly or those subjected to bed rest or immobilization due to surgery or chronic disease."
On 8 April 2016, Rodent Research 3 delivered 20 mice on SpaceX CRS-8. The experiment sponsored by Eli Lilly and Co. was a study of myostatin inhibition for the prevention of skeletal and muscle atrophy and weakness. Mice are known to have rapid loss of muscle and bone mass after as little as 12 days of space flight exposure. The mice were euthanized and dissected on the station and then frozen for eventual return to Earth for further study.
On 29 June 2018, a SpaceX Dragon spaceship blasted off from Florida carrying 20 mice. The rodent crew arrived at the ISS on 2 July 2018. Their record-breaking journey – this was the longest mice have been off the planet – was part of a study on how Earth-dwellers' physiology and sleep schedules responded to the stress of being in space.
The Chinese lunar lander Chang'e 4 carries a 3 kg sealed container with seeds and insect eggs to test whether plants and insects could hatch and grow together in synergy. The experiment includes six types of organisms: cottonseed, potato, rapeseed, Arabidopsis thaliana (a flowering plant), as well as yeast and fruit fly eggs. If the eggs hatch, the larvae would produce carbon dioxide, while the germinated plants would release oxygen through photosynthesis. A miniature camera is imaging the growth.
On 11 April 2019, the Israeli spacecraft Beresheet crashed into the Moon during a failed landing attempt. Its payload included a few thousand tardigrades. They could potentially survive on the lunar surface for some years, although it is unclear if they survived the impact.
2020s
On 3 June 2021, SpaceX CRS-22 launched tardigrades (water bears) and Hawaiian bobtail squid to the ISS. The squid were launched as hatchlings and will be studied to see if they can incorporate their symbiotic bacteria into their light organ while in space.
See also
Alice King Chatham – American designer who designed equipment for some of the first animals in space
Félicette, only cat in space
Félix I, a canceled Brazilian Army project to launch a cat in 1958-59.
List of microorganisms tested in outer space
List of species that have landed on the Moon
One Small Step: The Story of the Space Chimps, 2008 documentary
Parachuting animals
Space Dogs, 2010 film
Tardigrades on the Moon
References
Further reading
Caswell, Kurt. 2018. Laika's window: The legacy of a Soviet space dog. San Antonio: Trinity University Press.
L. W. Fraser and E. H. Siegler, High Altitude Research Using the V-2 Rocket, March 1946 – April 1947 (Johns Hopkins University, Bumblebee Series Report No. 8, July 1948), p. 90.
Kenneth W. Gatland, Development of the Guided Missile (London and New York, 1952), p. 188
Capt. David G. Simons, Use of V-2 Rocket to Convey Primate to Upper Atmosphere (Wright-Patterson Air Force Base, AF Technical Report 5821, May 1949), p. 1.
Lloyd Mallan, Men, Rockets, and Space Rats (New York, 1955), pp. 84–93.
External links
History of chimpanzees in U.S. air and space research
History of Research in Space Biology and Biodynamics (NASA)
One Small Step: The Story of the Space Chimps. Documentary on History of Primates Used in Space Travel
Purr 'n' Fur: Felicette and Felix, Space Cats
Animal keeping by humans
Articles containing video clips | Animals in space | [
"Chemistry",
"Biology"
] | 5,212 | [
"Animal testing",
"Space-flown life",
"Animals in space"
] |
600,782 | https://en.wikipedia.org/wiki/LinuxChix | LinuxChix is a women-oriented Linux community. It was formed to provide both technical and social support for women Linux users, although men are encouraged to contribute. Members of the community are referred to as "a Linux chick" (singular) and "LinuxChix" or "Linux Chix" (plural) regardless of gender.
History
LinuxChix was founded in 1999 by Deb Richardson, who was a technical writer and web-master at an open source consulting firm. Her reason for founding LinuxChix was to create an alternative to the "locker room mentality" of some other Linux User Groups and forums. There are two core rules: "be polite and be helpful."
LinuxChix started as an electronic mailing list called grrltalk. The growth of this mailing list led to the establishment of other mailing lists, beginning with techtalk for technical discussions and issues for discussion of women's political issues. LinuxChix received attention when ZDNet published an article on it, which was subsequently cross-posted on Slashdot.
Leadership and structure
Deb Richardson oversaw the activities of LinuxChix until 2001, when she handed over global coordination and hosting to Melbourne programmer and writer Jenn Vesperman. Jenn Vesperman led the community in a mostly hands-off fashion, delegating almost all tasks, including mailing list administration and website maintenance, to a group of volunteers. During Jenn Vesperman's tenure, the number of mailing lists tripled with the newchix mailing list for those new to Linux, the courses mailing list used by LinuxChix to teach each other specific topics, and the grrls-only mailing list (the only list closed to male subscribers) founded by Val Henson in 2002. At around the same time, a LinuxChix IRC server was created.
The term LinuxChix refers to the organisation centered on the official website, the mailing lists and the IRC channels. The organisation has no official status, and the name is used by other loosely affiliated groups, including several local, continental, and national chapters which operate independently.
In March 2007, Jenn Vesperman announced that she was retiring as the coordinator and invited nominations for a new leader. Mary Gardiner was announced as the new coordinator In April 2007, planning to serve as coordinator until 2009, however she resigned in June 2007. Currently the organization is led by three lead volunteers known as the "Tres Chix" who are elected by popular vote. In August 2007, Sulamita Garcia, Akkana Peck and Carla Schroder were elected to these positions.
Regional chapters
LinuxChix has over 15 regional chapters around the world. In 2004, a chapter was founded in Africa. In March 2007, on the International Women's Day, Australia's two LinuxChix chapters united to form a nationwide chapter called "AussieChix". The New Zealand chapter was established in February 2007.
Events
Some local LinuxChix chapters hold regular meetings. Others only meet up on special occasions, such as visits from non-local members or in conjunction with technical conferences. In 2007, members of the Sydney chapter organized a LinuxChix miniconf at linux.conf.au at the University of New South Wales. Events are held on other special occasions; in 2005, for example, LinuxChix Africa organized an event to celebrate Software Freedom Day at Wits University.
LinuxChix labs
The Indian chapter of LinuxChix (aka IndiChix) led an initiative to establish Linux labs in a number of cities in India. These labs provide spaces equipped with PCs and internet connections where women can learn more about Linux and collaborate on contributions to the Libre software community. Labs have gone live in Bangalore, Delhi, Mumbai, and Pune.
See also
Ada Initiative
National Center for Women & Information Technology
Anita Borg Institute for Women and Technology
Girl Geek Dinners
References
External links
LinuxChix website
LinuxChix regional chapters
Women in computing
Electronic mailing lists
Free and open-source software organizations
Internet properties established in 1999
Linux user groups
Organizations for women in science and technology | LinuxChix | [
"Technology"
] | 835 | [
"Organizations for women in science and technology",
"Women in science and technology"
] |
600,788 | https://en.wikipedia.org/wiki/Brain-derived%20neurotrophic%20factor | Brain-derived neurotrophic factor (BDNF), or abrineurin, is a protein that, in humans, is encoded by the BDNF gene. BDNF is a member of the neurotrophin family of growth factors, which are related to the canonical nerve growth factor (NGF), a family which also includes NT-3 and NT-4/NT-5. Neurotrophic factors are found in the brain and the periphery. BDNF was first isolated from a pig brain in 1982 by Yves-Alain Barde and Hans Thoenen.
BDNF activates the TrkB tyrosine kinase receptor.
Function
BDNF acts on certain neurons of the central nervous system and the peripheral nervous system expressing TrkB, helping to support survival of existing neurons, and encouraging growth and differentiation of new neurons and synapses. In the brain it is active in the hippocampus, cortex, and basal forebrain—areas vital to learning, memory, and higher thinking. BDNF is also expressed in the retina, kidneys, prostate, motor neurons, and skeletal muscle, and is also found in saliva.
BDNF itself is important for long-term memory.
Although the vast majority of neurons in the mammalian brain are formed prenatally, parts of the adult brain retain the ability to grow new neurons from neural stem cells in a process known as neurogenesis. Neurotrophins are proteins that help to stimulate and control neurogenesis, BDNF being one of the most active. Mice born without the ability to make BDNF have developmental defects in the brain and sensory nervous system, and usually die soon after birth, suggesting that BDNF plays an important role in normal neural development. Other important neurotrophins structurally related to BDNF include NT-3, NT-4, and NGF.
BDNF is made in the endoplasmic reticulum and secreted from dense-core vesicles. It binds carboxypeptidase E (CPE), and disruption of this binding has been proposed to cause the loss of sorting BDNF into dense-core vesicles. The phenotype for BDNF knockout mice can be severe, including postnatal lethality. Other traits include sensory neuron losses that affect coordination, balance, hearing, taste, and breathing. Knockout mice also exhibit cerebellar abnormalities and an increase in the number of sympathetic neurons.
Certain types of physical exercise have been shown to markedly (threefold) increase BDNF synthesis in the human brain, a phenomenon which is partly responsible for exercise-induced neurogenesis and improvements in cognitive function. Niacin appears to upregulate BDNF and tropomyosin receptor kinase B (TrkB) expression as well.
Mechanism of action
BDNF binds at least two receptors on the surface of cells that are capable of responding to this growth factor, TrkB (pronounced "Track B") and the LNGFR (for low-affinity nerve growth factor receptor, also known as p75). It may also modulate the activity of various neurotransmitter receptors, including the Alpha-7 nicotinic receptor. BDNF has also been shown to interact with the reelin signaling chain. The expression of reelin by Cajal–Retzius cells goes down during development under the influence of BDNF. The latter also decreases reelin expression in neuronal culture.
TrkB
The TrkB receptor is encoded by the NTRK2 gene and is member of a receptor family of tyrosine kinases that includes TrkA and TrkC. TrkB autophosphorylation is dependent upon its ligand-specific association with BDNF, a widely expressed activity-dependent neurotrophic factor that regulates plasticity and is dysregulated following hypoxic injury. The activation of the BDNF-TrkB pathway is important in the development of short-term memory and the growth of neurons.
LNGFR
The role of the other BDNF receptor, p75, is less clear. While the TrkB receptor interacts with BDNF in a ligand-specific manner, all neurotrophins can interact with the p75 receptor. When the p75 receptor is activated, it leads to activation of NFkB receptor. Thus, neurotrophic signaling may trigger apoptosis rather than survival pathways in cells expressing the p75 receptor in the absence of Trk receptors. Recent studies have revealed a truncated isoform of the TrkB receptor (t-TrkB) may act as a dominant negative to the p75 neurotrophin receptor, inhibiting the activity of p75, and preventing BDNF-mediated cell death.
Expression
The BDNF protein is encoded by a gene that is also called BDNF, found in humans on chromosome 11. Structurally, BDNF transcription is controlled by eight different promoters, each leading to different transcripts containing one of eight untranslated 5' exons (I to VIII) spliced to the 3' encoding exon. Promoter IV activity, leading to the translation of exon IV-containing mRNA, is strongly stimulated by calcium and is primarily under the control of a Cre regulatory component, suggesting a putative role for the transcription factor CREB and the source of BDNF's activity-dependent effects .
There are multiple mechanisms through neuronal activity that can increase BDNF exon IV specific expression. Stimulus-mediated neuronal excitation can lead to NMDA receptor activation, triggering a calcium influx. Through a protein signaling cascade requiring Erk, CaM KII/IV, PI3K, and PLC, NMDA receptor activation is capable of triggering BDNF exon IV transcription. BDNF exon IV expression also seems capable of further stimulating its own expression through TrkB activation. BDNF is released from the post-synaptic membrane in an activity-dependent manner, allowing it to act on local TrkB receptors and mediate effects that can lead to signaling cascades also involving Erk and CaM KII/IV. Both of these pathways probably involve calcium-mediated phosphorylation of CREB at Ser133, thus allowing it to interact with BDNF's Cre regulatory domain and upregulate transcription. However, NMDA-mediated receptor signaling is probably necessary to trigger the upregulation of BDNF exon IV expression because normally CREB interaction with CRE and the subsequent translation of the BDNF transcript is blocked by of the basic helix–loop–helix transcription factor protein 2 (BHLHB2). NMDA receptor activation triggers the release of the regulatory inhibitor, allowing for BDNF exon IV upregulation to take place in response to the activity-initiated calcium influx. Activation of dopamine receptor D5 also promotes expression of BDNF in prefrontal cortex neurons.
Common SNPs in BDNF gene
BDNF has several known single nucleotide polymorphisms (SNP), including, but not limited to, rs6265, C270T, rs7103411, rs2030324, rs2203877, rs2049045 and rs7124442. As of 2008, rs6265 is the most investigated SNP of the BDNF gene.
Val66Met
A common SNP in the BDNF gene is rs6265. This point mutation in the coding sequence, a guanine to adenine switch at position 196, results in an amino acid switch: valine to methionine exchange at codon 66, Val66Met, which is in the prodomain of BDNF. Val66Met is unique to humans.
The mutation interferes with normal translation and intracellular trafficking of BDNF mRNA, as it destabilizes the mRNA and renders it prone to degradation. The proteins resulting from mRNA that does get translated, are not trafficked and secreted normally, as the amino acid change occurs on the portion of the prodomain where sortilin binds; and sortilin is essential for normal trafficking.
The Val66Met mutation results in a reduction of hippocampal tissue and has since been reported in a high number of individuals with learning and memory disorders, anxiety disorders, major depression, and neurodegenerative diseases such as Alzheimer's and Parkinson's.
A meta-analysis indicates that the BDNF Val66Met variant is not associated with serum BDNF.
Role in synaptic transmission
Glutamatergic signaling
Glutamate is the brain's major excitatory neurotransmitter and its release can trigger the depolarization of postsynaptic neurons. AMPA and NMDA receptors are two ionotropic glutamate receptors involved in glutamatergic neurotransmission and essential to learning and memory via long-term potentiation. While AMPA receptor activation leads to depolarization via sodium influx, NMDA receptor activation by rapid successive firing allows calcium influx in addition to sodium. The calcium influx triggered through NMDA receptors can lead to expression of BDNF, as well as other genes thought to be involved in LTP, dendritogenesis, and synaptic stabilization.
NMDA receptor activity
NMDA receptor activation is essential to producing the activity-dependent molecular changes involved in the formation of new memories. Following exposure to an enriched environment, BDNF and NR1 phosphorylation levels are upregulated simultaneously, probably because BDNF is capable of phosphorylating NR1 subunits, in addition to its many other effects. One of the primary ways BDNF can modulate NMDA receptor activity is through phosphorylation and activation of the NMDA receptor one subunit, particularly at the PKC Ser-897 site. The mechanism underlying this activity is dependent upon both ERK and PKC signaling pathways, each acting individually, and all NR1 phosphorylation activity is lost if the TrKB receptor is blocked. PI3 kinase and Akt are also essential in BDNF-induced potentiation of NMDA receptor function and inhibition of either molecule eliminated receptor BDNF can also increase NMDA receptor activity through phosphorylation of the NR2B subunit. BDNF signaling leads to the autophosphorylation of the intracellular domain of the TrkB receptor (ICD-TrkB). Upon autophosphorylation, Fyn associates with the pICD-TrkB through its Src homology domain 2 (SH2) and is phosphorylated at its Y416 site. Once activated, Fyn can bind to NR2B through its SH2 domain and mediate phosphorylation of its Tyr-1472 site. Similar studies have suggested Fyn is also capable of activating NR2A although this was not found in the hippocampus. Thus, BDNF can increase NMDA receptor activity through Fyn activation. This has been shown to be important for processes such as spatial memory in the hippocampus, demonstrating the therapeutic and functional relevance of BDNF-mediated NMDA receptor activation.
Synapse stability
In addition to mediating transient effects on NMDAR activation to promote memory-related molecular changes, BDNF should also initiate more stable effects that could be maintained in its absence and not depend on its expression for long term synaptic support.
It was previously mentioned that AMPA receptor expression is essential to learning and memory formation, as these are the components of the synapse that will communicate regularly and maintain the synapse structure and function long after the initial activation of NMDA channels. BDNF is capable of increasing the mRNA expression of GluR1 and GluR2 through its interaction with the TrkB receptor and promoting the synaptic localization of GluR1 via PKC- and CaMKII-mediated Ser-831 phosphorylation. It also appears that BDNF is able to influence Gl1 activity through its effects on NMDA receptor activity. BDNF significantly enhanced the activation of GluR1 through phosphorylation of tyrosine830, an effect that was abolished in either the presence of a specific NR2B antagonist or a trk receptor tyrosine kinase inhibitor. Thus, it appears BDNF can upregulate the expression and synaptic localization of AMPA receptors, as well as enhance their activity through its postsynaptic interactions with the NR2B subunit. This suggests BDNF is not only capable of initiating synapse formation through its effects on NMDA receptor activity, but it can also support the regular every-day signaling necessary for stable memory function.
GABAergic signaling
One mechanism through which BDNF appears to maintain elevated levels of neuronal excitation is through preventing GABAergic signaling activities. While glutamate is the brain's major excitatory neurotransmitter and phosphorylation normally activates receptors, GABA is the brain's primary inhibitory neurotransmitter and phosphorylation of GABAA receptors tend to reduce their activity. Blockading BDNF signaling with a tyrosine kinase inhibitor or a PKC inhibitor in wild type mice produced significant reductions in spontaneous action potential frequencies that were mediated by an increase in the amplitude of GABAergic inhibitory postsynaptic currents (IPSC). Similar effects could be obtained in BDNF knockout mice, but these effects were reversed by local application of BDNF.
This suggests BDNF increases excitatory synaptic signaling partly through the post-synaptic suppression of GABAergic signaling by activating PKC through its association with TrkB. Once activated, PKC can reduce the amplitude of IPSCs through to GABAA receptor phosphorylation and inhibition. In support of this putative mechanism, activation of PKCε leads to phosphorylation of N-ethylmaleimide-sensitive factor (NSF) at serine 460 and threonine 461, increasing its ATPase activity which downregulates GABAA receptor surface expression and subsequently attenuates inhibitory currents.
Synaptogenesis
BDNF also enhances synaptogenesis. Synaptogenesis is dependent upon the assembly of new synapses and the disassembly of old synapses by β-adducin. Adducins are membrane-skeletal proteins that cap the growing ends of actin filaments and promote their association with spectrin, another cytoskeletal protein, to create stable and integrated cytoskeletal networks. Actins have a variety of roles in synaptic functioning. In pre-synaptic neurons, actins are involved in synaptic vesicle recruitment and vesicle recovery following neurotransmitter release. In post-synaptic neurons they can influence dendritic spine formation and retraction as well as AMPA receptor insertion and removal. At their C-terminus, adducins possess a myristoylated alanine-rich C kinase substrate (MARCKS) domain which regulates their capping activity. BDNF can reduce capping activities by upregulating PKC, which can bind to the adducing MRCKS domain, inhibit capping activity, and promote synaptogenesis through dendritic spine growth and disassembly and other activities.
Dendritogenesis
Local interaction of BDNF with the TrkB receptor on a single dendritic segment is able to stimulate an increase in PSD-95 trafficking to other separate dendrites as well as to the synapses of locally stimulated neurons. PSD-95 localizes the actin-remodeling GTPases, Rac and Rho, to synapses through the binding of its PDZ domain to kalirin, increasing the number and size of spines. Thus, BDNF-induced trafficking of PSD-95 to dendrites stimulates actin remodeling and causes dendritic growth in response to BDNF.
Neurogenesis
Laboratory studies indicate that BDNF may play a role in neurogenesis. BDNF can promote protective pathways and inhibit damaging pathways in the NSCs and NPCs that contribute to the brain's neurogenic response by enhancing cell survival. This becomes especially evident following suppression of TrkB activity. TrkB inhibition results in a 2–3 fold increase in cortical precursors displaying EGFP-positive condensed apoptotic nuclei and a 2–4 fold increase in cortical precursors that stained immunopositive for cleaved caspase-3. BDNF can also promote NSC and NPC proliferation through Akt activation and PTEN inactivation. Some studies suggest that BDNF may promote neuronal differentiation.
Research
Preliminary research has focused on the possible links between BDNF and clinical conditions, such as depression, schizophrenia, and Alzheimer's disease.
Schizophrenia
Preliminary studies have assessed a possible relationship between schizophrenia and BDNF. It has been shown that BDNF mRNA levels are decreased in cortical layers IV and V of the dorsolateral prefrontal cortex of schizophrenic patients, an area associated with working memory.
Depression
The neurotrophic hypothesis of depression states that depression is associated with a decrease in the levels of BDNF.
Epilepsy
Levels of both BDNF mRNA and BDNF protein are known to be up-regulated in epilepsy.
See also
Epigenetics of depression § Brain-derived neurotrophic factor
Epigenetics of schizophrenia § Methylation of BDNF
Tropomyosin receptor kinase B § Agonists
References
External links
Neurotrophic factors
Peptide hormones
Growth factors
Developmental neuroscience
TrkB agonists | Brain-derived neurotrophic factor | [
"Chemistry"
] | 3,869 | [
"Neurochemistry",
"Neurotrophic factors",
"Growth factors",
"Signal transduction"
] |
600,805 | https://en.wikipedia.org/wiki/Innuendo | An innuendo is a hint, insinuation or intimation about a person or thing, especially of a denigrating or derogatory nature. It can also be a remark or question, typically disparaging (also called insinuation), that works obliquely by allusion. In the latter sense, the intention is often to insult or accuse someone in such a way that one's words, taken literally, are innocent.
According to the Advanced Oxford Learner's Dictionary, an innuendo is "an indirect remark about somebody or something, usually suggesting something bad, mean or rude", such as: "innuendos about her private life" or "The song is full of sexual innuendo".
Sexual innuendo
The term sexual innuendo has acquired a specific meaning, namely that of a "risqué" double entendre by playing on a possibly sexual interpretation of an otherwise innocent uttering. For example: "We need to go deeper" can be seen as either a request for further inquiry or allude to sexual penetration.
Defamation law
In the context of defamation law, an innuendo meaning is one which is not directly contained in the words that are illustrated, but which would be understood by those reading it based on specialized knowledge.
Film, television, and other media
Comedy film scripts have used innuendo since the beginning of sound film itself. A notable example is the Carry On film series (1958–1992) in which innuendo was a staple feature, often including the title of the film itself. British sitcoms and comedy shows such as Are You Being Served? and Round the Horne have also made extensive use of innuendo. Mild sexual innuendo is a staple of British pantomime.
Numerous television programs and animated films targeted at child audiences often use innuendos in an attempt to entertain adolescent/adult audiences without exceeding their network's censorship policies. For example, Rocko's Modern Life employed numerous innuendos over its run, such as alluding to masturbation by naming the fictional fast food chain in the show "Chokey Chicken". Over 20 percent of the show's audience were adults as a result.
On The Scott Mills Show on BBC Radio 1, listeners are asked to send in clips from radio and TV with innuendos in a humorous context, a feature known as "Innuendo Bingo". Presenters and special guests fill their mouths with water and listen to the clips, and the last person to spit the water out with laughter wins the game.
See also
Blind item
Doublespeak
Euphemism
Roman à clef
References
Comedy
Rhetorical techniques
Sociolinguistics
Harassment and bullying | Innuendo | [
"Biology"
] | 550 | [
"Harassment and bullying",
"Behavior",
"Aggression"
] |
600,835 | https://en.wikipedia.org/wiki/Canada%20balsam | Canada balsam, also called Canada turpentine or balsam of fir, is the oleoresin of the balsam fir tree (Abies balsamea) of boreal North America. The resin, dissolved in essential oils, is a viscous, sticky, colourless or yellowish liquid that turns to a transparent yellowish mass when the essential oils have been allowed to evaporate.
Canada balsam is amorphous when dried. It has poor thermal and solvent resistance.
Uses
Due to its high optical quality and the similarity of its refractive index to that of crown glass (n = 1.55), purified and filtered Canada balsam was traditionally used in optics as an invisible-when-dry glue for glass, such as lens elements. Other optical elements can be cemented with Canada balsam, such as two prisms bonded to form a beam splitter.
Canada balsam was also commonly used for making permanent microscope slides. From about 1830 molten Canada balsam was used for microscope slides. Canada balsam in solution was then introduced in 1843, becoming popular in the 1850s. In biology, for example, it can be used to conserve microscopic samples by sandwiching the sample between a microscope slide and a glass coverslip, using Canada balsam to glue the arrangement together and enclose the sample to conserve it.
Canada balsam dissolved in xylene is also used for preparing slide mounts. Some workers prefer terpene resin for slide mounts, as it is both less acidic and cheaper than balsam.
Another important application of Canada balsam is in the construction of the Nicol prism. A Nicol prism consists of a calcite crystal cut into two halves. Canada balsam is placed between the two layers. Calcite is an anisotropic crystal and has different refractive indices for rays polarized along directions parallel and perpendicular to its optic axis. These rays with differing refractive indices are known as the ordinary and extraordinary rays. The refractive index for Canada balsam is in between the refractive index for the ordinary and extraordinary rays. Hence the ordinary ray will be totally internally reflected. The emergent ray will be linearly polarized, and traditionally this has been one of the popular ways of producing polarized light.
Some other uses (traditional and current) include:
In geology, it is used as a common thin section cement and glue and for refractive-index studies and tests, such as the Becke line test;
To fix scratches in glass (car glass, for instance) as invisibly as possible;
In oil painting, to achieve glow and facilitate fusion;
In Buckley's cough syrup.
Balsam was phased out as an optical adhesive during World War II, in favour of polyester, epoxy, and urethane-based adhesives. In modern optical manufacturing, UV-cured epoxies are often used to bond lens elements. Synthetic resins have largely replaced organic balsams for use in slide mounts.
See also
Balm of Gilead, a healing compound made from the resinous gum of Commiphora gileadensis.
References
Adhesives
Resins
Microscopy mountants | Canada balsam | [
"Physics",
"Chemistry"
] | 641 | [
"Resins",
"Unsolved problems in physics",
"Microscopy",
"Microscopy mountants",
"Amorphous solids"
] |
600,892 | https://en.wikipedia.org/wiki/Arbitrary-precision%20arithmetic | In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.
Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should not be confused with the symbolic computation provided by many computer algebra systems, which represent numbers by expressions such as , and can thus represent any computable number with infinite precision.
Applications
A common application is public-key cryptography, whose algorithms commonly employ arithmetic with integers having hundreds of digits. Another is in situations where artificial limits and overflows would be inappropriate. It is also useful for checking the results of fixed-precision calculations, and for determining optimal or near-optimal values for coefficients needed in formulae, for example the that appears in Gaussian integration.
Arbitrary precision arithmetic is also used to compute fundamental mathematical constants such as π to millions or more digits and to analyze the properties of the digit strings or more generally to investigate the precise behaviour of functions such as the Riemann zeta function where certain questions are difficult to explore via analytical methods. Another example is in rendering fractal images with an extremely high magnification, such as those found in the Mandelbrot set.
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too large to represent at the fixed level of precision. Some processors can instead deal with overflow by saturation, which means that if a result would be unrepresentable, it is replaced with the nearest representable value. (With 16-bit unsigned saturation, adding any positive amount to 65535 would yield 65535.) Some processors can generate an exception if an arithmetic result exceeds the available precision. Where necessary, the exception can be caught and recovered from—for instance, the operation could be restarted in software using arbitrary-precision arithmetic.
In many cases, the task or the programmer can guarantee that the integer values in a specific application will not grow large enough to cause an overflow. Such guarantees may be based on pragmatic limits: a school attendance program may have a task limit of 4,000 students. A programmer may design the computation so that intermediate results stay within specified precision boundaries.
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow. It also makes it possible to guarantee that arithmetic results will be the same on all machines, regardless of any particular machine's word size. The exclusive use of arbitrary-precision numbers in a programming language also simplifies the language, because a number is a number and there is no need for multiple types to represent different levels of precision.
Implementation issues
Arbitrary-precision arithmetic is considerably slower than arithmetic using numbers that fit entirely within processor registers, since the latter are usually implemented in hardware arithmetic whereas the former must be implemented in software. Even if the computer lacks hardware for certain operations (such as integer division, or all floating-point operations) and software is provided instead, it will use number sizes closely related to the available hardware registers: one or two words only. There are exceptions, as certain variable word length machines of the 1950s and 1960s, notably the IBM 1620, IBM 1401 and the Honeywell 200 series, could manipulate numbers bound only by available storage, with an extra bit that delimited the value.
Numbers can be stored in a fixed-point format, or in a floating-point format as a significand multiplied by an arbitrary exponent. However, since division almost immediately introduces infinitely repeating sequences of digits (such as 4/7 in decimal, or 1/10 in binary), should this possibility arise then either the representation would be truncated at some satisfactory size or else rational numbers would be used: a large integer for the numerator and for the denominator. But even with the greatest common divisor divided out, arithmetic with rational numbers can become unwieldy very quickly: 1/99 − 1/100 = 1/9900, and if 1/101 is then added, the result is 10001/999900.
The size of arbitrary-precision numbers is limited in practice by the total storage available, and computation time.
Numerous algorithms have been developed to efficiently perform arithmetic operations on numbers stored with arbitrary precision. In particular, supposing that digits are employed, algorithms have been designed to minimize the asymptotic complexity for large .
The simplest algorithms are for addition and subtraction, where one simply adds or subtracts the digits in sequence, carrying as necessary, which yields an algorithm (see big O notation).
Comparison is also very simple. Compare the high-order digits (or machine words) until a difference is found. Comparing the rest of the digits/words is not necessary. The worst case is , but it may complete much faster with operands of similar magnitude.
For multiplication, the most straightforward algorithms used for multiplying numbers by hand (as taught in primary school) require operations, but multiplication algorithms that achieve complexity have been devised, such as the Schönhage–Strassen algorithm, based on fast Fourier transforms, and there are also algorithms with slightly worse complexity but with sometimes superior real-world performance for smaller . The Karatsuba multiplication is such an algorithm.
For division, see division algorithm.
For a list of algorithms along with complexity estimates, see computational complexity of mathematical operations.
For examples in x86 assembly, see external links.
Pre-set precision
In some languages such as REXX and ooRexx, the precision of all calculations must be set before doing a calculation. Other languages, such as Python and Ruby, extend the precision automatically to prevent overflow.
Example
The calculation of factorials can easily produce very large numbers. This is not a problem for their usage in many formulas (such as Taylor series) because they appear along with other terms, so that—given careful attention to the order of evaluation—intermediate calculation values are not troublesome. If approximate values of factorial numbers are desired, Stirling's approximation gives good results using floating-point arithmetic. The largest representable value for a fixed-size integer variable may be exceeded even for relatively small arguments as shown in the table below. Even floating-point numbers are soon outranged, so it may help to recast the calculations in terms of the logarithm of the number.
But if exact values for large factorials are desired, then special software is required, as in the pseudocode that follows, which implements the classic algorithm to calculate 1, 1×2, 1×2×3, 1×2×3×4, etc. the successive factorial numbers.
constants:
Limit = 1000 % Sufficient digits.
Base = 10 % The base of the simulated arithmetic.
FactorialLimit = 365 % Target number to solve, 365!
tdigit: Array[0:9] of character = ["0","1","2","3","4","5","6","7","8","9"]
variables:
digit: Array[1:Limit] of 0..9 % The big number.
carry, d: Integer % Assistants during multiplication.
last: Integer % Index into the big number's digits.
text: Array[1:Limit] of character % Scratchpad for the output.
digit[*] := 0 % Clear the whole array.
last := 1 % The big number starts as a single-digit,
digit[1] := 1 % its only digit is 1.
for n := 1 to FactorialLimit: % Step through producing 1!, 2!, 3!, 4!, etc.
carry := 0 % Start a multiply by n.
for i := 1 to last: % Step along every digit.
d := digit[i] * n + carry % Multiply a single digit.
digit[i] := d mod Base % Keep the low-order digit of the result.
carry := d div Base % Carry over to the next digit.
while carry > 0: % Store the remaining carry in the big number.
if last >= Limit: error("overflow")
last := last + 1 % One more digit.
digit[last] := carry mod Base
carry := carry div Base % Strip the last digit off the carry.
text[*] := " " % Now prepare the output.
for i := 1 to last: % Translate from binary to text.
text[Limit - i + 1] := tdigit[digit[i]] % Reversing the order.
print text[Limit - last + 1:Limit], " = ", n, "!"
With the example in view, a number of details can be discussed. The most important is the choice of the representation of the big number. In this case, only integer values are required for digits, so an array of fixed-width integers is adequate. It is convenient to have successive elements of the array represent higher powers of the base.
The second most important decision is in the choice of the base of arithmetic, here ten. There are many considerations. The scratchpad variable must be able to hold the result of a single-digit multiply plus the carry from the prior digit's multiply. In base ten, a sixteen-bit integer is certainly adequate as it allows up to 32767. However, this example cheats, in that the value of is not itself limited to a single digit. This has the consequence that the method will fail for or so. In a more general implementation, would also use a multi-digit representation. A second consequence of the shortcut is that after the multi-digit multiply has been completed, the last value of carry may need to be carried into multiple higher-order digits, not just one.
There is also the issue of printing the result in base ten, for human consideration. Because the base is already ten, the result could be shown simply by printing the successive digits of array digit, but they would appear with the highest-order digit last (so that 123 would appear as "321"). The whole array could be printed in reverse order, but that would present the number with leading zeroes ("00000...000123") which may not be appreciated, so this implementation builds the representation in a space-padded text variable and then prints that. The first few results (with spacing every fifth digit and annotation added here) are:
This implementation could make more effective use of the computer's built in arithmetic. A simple escalation would be to use base 100 (with corresponding changes to the translation process for output), or, with sufficiently wide computer variables (such as 32-bit integers) we could use larger bases, such as 10,000. Working in a power-of-2 base closer to the computer's built-in integer operations offers advantages, although conversion to a decimal base for output becomes more difficult. On typical modern computers, additions and multiplications take constant time independent of the values of the operands (so long as the operands fit in single machine words), so there are large gains in packing as much of a bignumber as possible into each element of the digit array. The computer may also offer facilities for splitting a product into a digit and carry without requiring the two operations of mod and div as in the example, and nearly all arithmetic units provide a carry flag which can be exploited in multiple-precision addition and subtraction. This sort of detail is the grist of machine-code programmers, and a suitable assembly-language bignumber routine can run faster than the result of the compilation of a high-level language, which does not provide direct access to such facilities but instead maps the high-level statements to its model of the target machine using an optimizing compiler.
For a single-digit multiply the working variables must be able to hold the value (base−1) + carry, where the maximum value of the carry is (base−1). Similarly, the variables used to index the digit array are themselves limited in width. A simple way to extend the indices would be to deal with the bignumber's digits in blocks of some convenient size so that the addressing would be via (block i, digit j) where i and j would be small integers, or, one could escalate to employing bignumber techniques for the indexing variables. Ultimately, machine storage capacity and execution time impose limits on the problem size.
History
IBM's first business computer, the IBM 702 (a vacuum-tube machine) of the mid-1950s, implemented integer arithmetic entirely in hardware on digit strings of any length from 1 to 511 digits. The earliest widespread software implementation of arbitrary-precision arithmetic was probably that in Maclisp. Later, around 1980, the operating systems VAX/VMS and VM/CMS offered bignum facilities as a collection of string functions in the one case and in the languages EXEC 2 and REXX in the other.
An early widespread implementation was available via the IBM 1620 of 1959–1970. The 1620 was a decimal-digit machine which used discrete transistors, yet it had hardware (that used lookup tables) to perform integer arithmetic on digit strings of a length that could be from two to whatever memory was available. For floating-point arithmetic, the mantissa was restricted to a hundred digits or fewer, and the exponent was restricted to two digits only. The largest memory supplied offered 60 000 digits, however Fortran compilers for the 1620 settled on fixed sizes such as 10, though it could be specified on a control card if the default was not satisfactory.
Software libraries
Arbitrary-precision arithmetic in most computer software is implemented by calling an external library that provides data types and subroutines to store numbers with the requested precision and to perform computations.
Different libraries have different ways of representing arbitrary-precision numbers, some libraries work only with integer numbers, others store floating point numbers in a variety of bases (decimal or binary powers). Rather than representing a number as single value, some store numbers as a numerator/denominator pair (rationals) and some can fully represent computable numbers, though only up to some storage limit. Fundamentally, Turing machines cannot represent all real numbers, as the cardinality of exceeds the cardinality of .
See also
Fürer's algorithm
Karatsuba algorithm
Mixed-precision arithmetic
Schönhage–Strassen algorithm
Toom–Cook multiplication
Little Endian Base 128
References
Further reading
, Section 4.3.1: The Classical Algorithms
, Chapter 9: Fast Algorithms for Large-Integer Arithmetic
External links
Chapter 9.3 of The Art of Assembly by Randall Hyde discusses multiprecision arithmetic, with examples in x86-assembly.
Rosetta Code task Arbitrary-precision integers Case studies in the style in which over 95 programming languages compute the value of 5**4**3**2 using arbitrary precision arithmetic.
Computer arithmetic
Computer arithmetic algorithms
Management cybernetics | Arbitrary-precision arithmetic | [
"Mathematics"
] | 3,303 | [
"Computer arithmetic",
"Arithmetic"
] |
600,925 | https://en.wikipedia.org/wiki/Propylene%20oxide | Propylene oxide is an acutely toxic and carcinogenic organic compound with the molecular formula C3H6O. This colourless volatile liquid with an odour similar to ether, is produced on a large scale industrially. Its major application is its use for the production of polyether polyols for use in making polyurethane plastics. It is a chiral epoxide, although it is commonly used as a racemic mixture.
This compound is sometimes called 1,2-propylene oxide to distinguish it from its isomer 1,3-propylene oxide, better known as oxetane.
Production
Industrial production of propylene oxide starts from propylene. Two general approaches are employed, one involving hydrochlorination and the other involving oxidation. In 2005, about half of the world production was through chlorohydrin technology and one half via oxidation routes. The latter approach is growing in importance.
Hydrochlorination route
The traditional route proceeds via the conversion of propene to propylene chlorohydrin according to the following simplified scheme:
The mixture of 1-chloro-2-propanol and 2-chloro-1-propanol is then dehydrochlorinated. For example:
Lime (calcium hydroxide) is often used to absorb the HCl.
Oxidation of propylene
The other general route to propylene oxide involves oxidation of propylene with an organic peroxide. The reaction follows this stoichiometry:
CH3CH=CH2 + RO2H → CH3CHCH2O + ROH
The process is practiced with four hydroperoxides:
In the Halcon process, t-Butyl hydroperoxide derived from oxygenation of isobutane, which affords t-butanol. This coproduct can be dehydrated to isobutene, converted to MTBE, an additive for gasoline.
Ethylbenzene hydroperoxide, derived from oxygenation of ethylbenzene, which affords 1-phenylethanol. This coproduct can be dehydrated to give styrene, a useful monomer.
Cumene hydroperoxide derived from oxygenation of cumene (isopropylbenzene), which affords cumyl alcohol. Via dehydration and hydrogenation this coproduct can be recycled back to cumene. This technology was commercialized by Sumitomo Chemical.
Hydrogen peroxide is the oxidant in the hydrogen peroxide to propylene oxide (HPPO) process, catalyzed by a titanium-doped silicalite:
C3H6 + H2O2 → C3H6O + H2O
In principle, this process produces only water as a side product. In practice, some ring-opened derivatives of PO are generated.
Propylene oxide is chiral building block that is commercially available in either enantiomeric form ((R)-(+) and (S)-(–)). The separated enantiomers can be obtained through a Co(III)-salen-catalyzed hydrolytic kinetic resolution of the racemic material.
Reactions
Like other epoxides, PO undergoes ring-opening reactions. With water, propylene glycol is produced. With alcohols, reactions, called hydroxylpropylation, analogous to ethoxylation occur. Grignard reagents add to propylene oxide to give secondary alcohols.
Some other reactions of propylene oxide include:
Reaction with aluminium oxide at 250–260 °C leads to propionaldehyde and a little acetone.
Reaction with silver(I) oxide leads to acetic acid.
Reaction with sodium–mercury amalgam and water leads to isopropanol.
Uses
Between 60 and 70% of all propylene oxide is converted to polyether polyols by the process called alkoxylation. These polyols are building blocks in the production of polyurethane plastics. About 20% of propylene oxide is hydrolyzed into propylene glycol, via a process which is accelerated by acid or base catalysis. Other major products are polypropylene glycol, propylene glycol ethers, and propylene carbonate.
Niche uses
Fumigant
The United States Food and Drug Administration has approved the use of propylene oxide to pasteurize raw almonds beginning on September 1, 2007, in response to two incidents of contamination by Salmonella in commercial orchards, one incident occurring in Canada and one in the United States.
Pistachio nuts can also be subjected to propylene oxide to control Salmonella.
Microscopy
Propylene oxide is commonly used in the preparation of biological samples for electron microscopy, to remove residual ethanol previously used for dehydration. In a typical procedure, the sample is first immersed in a mixture of equal volumes of ethanol and propylene oxide for 5 minutes, and then four times in pure oxide, 10 minutes each.
Munition
Propylene oxide is sometimes used in thermobaric munitions as the fuel in fuel–air explosives. In addition to the explosive damage from the blast wave, unexploded propylene oxide can cause additional effects from direct toxicity.
Safety
Propylene oxide is both acutely toxic and carcinogenic. Acute exposure causes respiratory tract irritation, eventually leading to death. Signs of toxicity after acute exposure include salivation, lacrimation, nasal discharge, gasping, lethargy and hypoactivity, weakness, and incoordination. Propylene oxide is also neurotoxic in rats, and presumably in humans. Propylene oxide alkylates DNA and is considered a mutagen for both animals and humans. Pregnant rats exposed to 500ppm of propylene oxide for less than 8 hours gave birth to litters with significant deformities and weight deficiencies. Similar exposure has also shown to reduce animal fertility. As such, it is a known animal carcinogen and potential human carcinogen, and is included into the List of IARC Group 2B carcinogens.
Propylene oxide is an extremely flammable liquid, and its vapors can form explosive mixtures with air at concentrations as low as 2.3% (Lower Explosive Limit). Propylene oxide vapor is twice as dense as air. When exposed to an open atmosphere, the vapor can accumulate in low-lying areas while spreading out over long distances and reach ignition source, causing flashback or an explosion. When heated, propylene oxide can rapidly self-polymerize and decompose producing other toxic gases such as carbon monoxide and various free radicals. Propylene oxide fires are especially dangerous and difficult for firefighters to extinguish. In a fire, sealed tanks of propylene oxide should be cooled with fire hoses to prevent explosion from self-polymerization. When burning in open air however, water can transport propylene oxide outside of the fire zone which can reignite upon floating to the surface. Additional firefighting measures should be taken to prevent propylene oxide from washing out to nearby drains and sewers contaminating the surrounding environment.
Natural occurrence
In 2016 it was reported that propylene oxide was detected in Sagittarius B2, a cloud of gas in the Milky Way weighing three million solar masses. It is the first chiral molecule to be detected in space, albeit with no enantiomeric excess.
References
Cited sources
External links
WebBook page for C3H6O
Propylene oxide at the United States Environmental Protection Agency
Propylene oxide – chemical product info: properties, production, applications.
Propylene oxide at the Technology Transfer Network Air Toxics Web Site
CDC – NIOSH Pocket Guide to Chemical Hazards
Epoxides
IARC Group 2B carcinogens
Commodity chemicals | Propylene oxide | [
"Chemistry"
] | 1,639 | [
"Commodity chemicals",
"Products of chemical industry"
] |
601,025 | https://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand%20dimension | In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a bounded set in a Euclidean space , or more generally in a metric space . It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.
To calculate this dimension for a fractal , imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer by applying a box-counting algorithm.
Suppose that is the number of boxes of side length required to cover the set. Then the box-counting dimension is defined as
Roughly speaking, this means that the dimension is the exponent such that , which is what one would expect in the trivial case where is a smooth space (a manifold) of integer dimension .
If the above limit does not exist, one may still take the limit superior and limit inferior, which respectively define the upper box dimension and lower box dimension. The upper box dimension is sometimes called the entropy dimension, Kolmogorov dimension, Kolmogorov capacity, limit capacity or upper Minkowski dimension, while the lower box dimension is also called the lower Minkowski dimension.
The upper and lower box dimensions are strongly related to the more popular Hausdorff dimension. Only in very special applications is it important to distinguish between the three (see below). Yet another measure of fractal dimension is the correlation dimension.
Alternative definitions
It is possible to define the box dimensions using balls, with either the covering number or the packing number. The covering number is the minimal number of open balls of radius required to cover the fractal, or in other words, such that their union contains the fractal. We can also consider the intrinsic covering number , which is defined the same way but with the additional requirement that the centers of the open balls lie in the set S. The packing number is the maximal number of disjoint open balls of radius one can situate such that their centers would be in the fractal. While , , and are not exactly identical, they are closely related to each other and give rise to identical definitions of the upper and lower box dimensions. This is easy to show once the following inequalities are proven:
These, in turn, follow either by definition or with little effort from the triangle inequality.
The advantage of using balls rather than squares is that this definition generalizes to any metric space. In other words, the box definition is extrinsic – one assumes the fractal space S is contained in a Euclidean space, and defines boxes according to the external geometry of the containing space. However, the dimension of S should be intrinsic, independent of the environment into which S is placed, and the ball definition can be formulated intrinsically. One defines an internal ball as all points of S within a certain distance of a chosen center, and one counts such balls to get the dimension. (More precisely, the Ncovering definition is extrinsic, but the other two are intrinsic.)
The advantage of using boxes is that in many cases N(ε) may be easily calculated explicitly, and that for boxes the covering and packing numbers (defined in an equivalent way) are equal.
The logarithm of the packing and covering numbers are sometimes referred to as entropy numbers and are somewhat analogous to the concepts of thermodynamic entropy and information-theoretic entropy, in that they measure the amount of "disorder" in the metric space or fractal at scale ε and also measure how many bits or digits one would need to specify a point of the space to accuracy ε.
Another equivalent (extrinsic) definition for the box-counting dimension is given by the formula
where for each r > 0, the set is defined to be the r-neighborhood of S, i.e. the set of all points in that are at distance less than r from S (or equivalently, is the union of all the open balls of radius r which have a center that is a member of S).
Properties
The upper box dimension is finitely stable, i.e. if {A1, ..., An} is a finite collection of sets, then
However, it is not countably stable, i.e. this equality does not hold for an infinite sequence of sets. For example, the box dimension of a single point is 0, but the box dimension of the collection of rational numbers in the interval [0, 1] has dimension 1. The Hausdorff dimension by comparison, is countably stable. The lower box dimension, on the other hand, is not even finitely stable.
An interesting property of the upper box dimension not shared with either the lower box dimension or the Hausdorff dimension is the connection to set addition. If A and B are two sets in a Euclidean space, then A + B is formed by taking all the pairs of points a, b where a is from A and b is from B and adding a + b. One has
Relations to the Hausdorff dimension
The box-counting dimension is one of a number of definitions for dimension that can be applied to fractals. For many well behaved fractals all these dimensions are equal; in particular, these dimensions coincide whenever the fractal satisfies the open set condition (OSC). For example, the Hausdorff dimension, lower box dimension, and upper box dimension of the Cantor set are all equal to log(2)/log(3). However, the definitions are not equivalent.
The box dimensions and the Hausdorff dimension are related by the inequality
In general, both inequalities may be strict. The upper box dimension may be bigger than the lower box dimension if the fractal has different behaviour in different scales. For example, examine the set of numbers in the interval [0, 1] satisfying the condition
The digits in the "odd place-intervals", i.e. between digits 22n+1 and 22n+2 − 1 are not restricted and may take any value. This fractal has upper box dimension 2/3 and lower box dimension 1/3, a fact which may be easily verified by calculating N(ε) for and noting that their values behave differently for n even and odd.
Another example: the set of rational numbers , a countable set with , has because its closure, , has dimension 1. In fact,
These examples show that adding a countable set can change box dimension, demonstrating a kind of instability of this dimension.
See also
Correlation dimension
Packing dimension
Uncertainty exponent
Weyl–Berry conjecture
Lacunarity
References
External links
FrakOut!: an OSS application for calculating the fractal dimension of a shape using the box counting method (Does not automatically place the boxes for you).
FracLac: online user guide and software ImageJ and FracLac box counting plugin; free user-friendly open source software for digital image analysis in biology
Fractals
Dimension theory
Hermann Minkowski | Minkowski–Bouligand dimension | [
"Mathematics"
] | 1,467 | [
"Mathematical analysis",
"Functions and mappings",
"Mathematical objects",
"Fractals",
"Mathematical relations"
] |
601,042 | https://en.wikipedia.org/wiki/United%20Kingdom%20Atomic%20Energy%20Authority | The United Kingdom Atomic Energy Authority is a UK government research organisation responsible for the development of fusion energy. It is an executive non-departmental public body of the Department for Energy Security and Net Zero (DESNZ).
The authority focuses on United Kingdom and European fusion energy research programmes at Culham in Oxfordshire, including the world's most powerful operating fusion device, the Joint European Torus (JET). The research aims to develop fusion power as a commercially viable, environmentally responsible energy source for the future.
A record 59 megajoules of sustained fusion energy was demonstrated by scientists and engineers working on JET in December 2021. In JET’s final deuterium-tritium experiments (DTE3), high fusion power was consistently produced for 5 seconds, resulting in a ground-breaking record of 69 megajoules using a mere 0.2 milligrams of fuel. JET has now ceased operating and decommissioning has commenced.
United Kingdom Atomic Energy Authority owns the Culham Science Centre and has a stake in the Harwell Campus, and is involved in the development of both sites as locations for science and innovation-based business.
On its formation in 1954, the authority was responsible for the United Kingdom's entire nuclear programme, both civil and defence, as well as the policing of nuclear sites. It made pioneering developments in nuclear (fission) power, overseeing the development of nuclear technology and performing much scientific research. However, since the early 1970s its areas of work have been gradually reduced, with functions transferred to other government organisations as well as to the private sector.
UKAEA has also been involved in undertaking safety and reliability assessments for outside bodies, due to its long running experience in such work within the nuclear field.
History
The authority was established on 19 July 1954 when the Atomic Energy Authority Act 1954 received royal assent and gave the authority the power "to produce, use and dispose of atomic energy and carry out research into any matters therewith".
The United Kingdom Atomic Energy Authority was formed from the Ministry of Supply, Department of Atomic Energy and inherited its facilities and most of its personnel on its formation.
The first chairman was Sir Edwin Plowden, with board members running the three major divisions:
Industrial Group: Sir Christopher Hinton
Research Group: Sir John Cockcroft
Weapons Group: Sir William Penney
The authority inherited nearly 20,000 employees, which doubled to 41,000 by 1961. Most of the authority's early activities were related to the United Kingdom's nuclear weapons programme, and the need for plutonium, highly enriched uranium, and materials for hydrogen bombs. Between 1952 and 1958 UKAEA carried out 21 nuclear weapon tests in Australia and the Pacific.
Following the Atomic Energy Authority Act 1971, the authority was split into three, with only research activities remaining with the authority. The Radiochemical Centre Ltd took over production of medical and industrial radioisotopes and was later privatised in 1982 as Amersham plc. British Nuclear Fuels Ltd (BNFL) took over nuclear fuel and weapons material producing activities: the manufacturing plant at Springfields, the enrichment plant at Capenhurst, the spent-fuel facility at Windscale, and the dual-purpose Calder Hall and Chapelcross military plutonium producing reactors.
The Atomic Energy Authority (Weapons Group) Act 1973 transferred responsibility for management of the UK's nuclear deterrent, including the Atomic Weapons Research Establishment at Aldermaston, directly to the Ministry of Defence.
In 1982 the authority was involved in the creation of Nirex, to develop and operate radioactive waste disposal facilities in the United Kingdom.
The Atomic Energy Authority Act 1986 put the authority into trading fund mode, requiring it to act and account as though it were a commercial enterprise and become self-financing.
The authority was then split again by the Atomic Energy Authority Act 1995, with the more commercial parts transferred into a public company AEA Technology, which was then floated on the London Stock Exchange in 1996. The nuclear facilities used for the UK's research and development programme, which held large decommissioning liabilities, were retained. The role of the authority became to decommission these nuclear assets and to restore the environment around the sites. From the early 1990s the authority completed more decommissioning work than anyone in Europe, and had considerable success in regenerating former nuclear sites for commercial use.
21st century
Following the Energy Act 2004, on 1 April 2005 the UK's specialist nuclear police force, the UK Atomic Energy Authority Constabulary, was reconstituted as the Civil Nuclear Constabulary. Responsibility for the force was also removed from the authority and transferred to the Civil Nuclear Police Authority. The 2004 Act also established the Nuclear Decommissioning Authority (NDA), which on 1 April 2005 took ownership and responsibility for the liabilities relating to the cleanup of UK nuclear sites. The authority became a contractor for the NDA for the decommissioning work at Dounreay, Harwell, Windscale, Winfrith and the JET facilities at Culham.
On 1 April 2008, the Authority announced a major re-structuring to meet its decommissioning obligations with the NDA. A new wholly owned subsidiary, UKAEA Limited, was formed with established expertise from the existing company, to focus on nuclear decommissioning and environmental restoration management and consultancy in the United Kingdom and international markets.
At the same time, Dounreay Site Restoration Limited (DSRL) was formed out of the existing Authority team at Dounreay and was licensed by the Health and Safety Executive to operate the site and carry out its decommissioning under the Authority's management. DSRL became a subsidiary of United Kingdom Atomic Energy Authority Limited.
In parallel with these changes, the site at Windscale in Cumbria was transferred to Sellafield Ltd, a site licence company under contract to the NDA, following close review and scrutiny by the Health and Safety Executive and environmental and security regulators. The majority of authority employees at the site transferred to Sellafield Ltd.
On 2 February 2009, the authority announced the next stage in restructuring. Research Sites Restoration Limited (RSRL), was formed from the existing teams at Harwell in Oxfordshire and Winfrith in Dorset and licensed by the Health and Safety Executive to operate those sites. RSRL continued the decommissioning programmes for Harwell and Winfrith on behalf of the NDA. RSRL also became a subsidiary of UKAEA Limited.
In October 2009, Babcock International Group plc acquired UKAEA Limited, the nuclear clean-up subsidiary of the authority, including its subsidiary companies DSRL and RSRL.
In 2009 the Culham Centre for Fusion Energy (CCFE) was launched as the new name for the home of United Kingdom fusion research.
In 2014 UKAEA announced the creation of a new branch of research, using expertise gained from the remote handling system created for JET to form a new centre for robotics known as RACE (Remote Applications in Challenging Environments).
The Authority has continued to expand its facilities at Culham in recent years, with the opening of a Materials Research Facility in 2016 and creation of the Oxfordshire Advanced Skills apprentice training centre.
Current activities
United Kingdom Atomic Energy Authority states its mission as "To lead the delivery of sustainable fusion energy and maximise the scientific and economic benefit." Its research programmes include a number of laboratories and other facilities at the Culham site.
Facilities and programmes
Culham Centre for Fusion Energy (CCFE)
The UK's national laboratory for fusion research, CCFE undertakes plasma theory and modelling studies to establish the physics basis for future fusion powerplants. It also studies the materials and engineering technology of tokamak fusion reactors. The centrepiece of CCFE's programme is the MAST Upgrade spherical tokamak experiment - the successor to the MAST device - which is expected to begin operation in 2019.
CCFE also operates and maintains the Joint European Torus (JET) for its research partners around Europe, and is a member of the co-ordinated R&D programme led by the EUROfusion consortium.
Materials Research Facility
UKAEA's Materials Research Facility carries out micro-characterisation of radioactive materials for researchers in both fusion energy and nuclear fission. It is open to users from academic and commercial organisations, aiming to bridge the gap between university laboratories and those at nuclear licensed sites. It is part of the National Nuclear Users' Facility and has received funding from the Henry Royce Institute. On the 14th of October 2022 the Materials Research Facility opened its extension.
Oxfordshire Advanced Skills
A partnership between United Kingdom Atomic Energy Authority and the Science & Technology Facilities Council, Oxfordshire Advanced Skills is an apprentice training centre located at Culham Science Centre. It offers training for technicians in engineering and hi-tech disciplines, with the intention of providing employers with highly skilled recruits ready to enter the workplace. Training is provided by the Manufacturing Technology Centre.
Remote Applications in Challenging Environments (RACE)
RACE is a test facility for robotics and autonomous systems. It grew out of UKAEA's remote handling operations at the JET nuclear fusion device, which date back to the 1990s. The UK Government funded the construction of the RACE centre at Culham with the intention of taking the knowledge gained at JET into other industries with 'challenging environments' where it is difficult for humans to perform work. RACE currently works with organisations in nuclear fusion and fission, with large physics facilities and with autonomous vehicle developers.
Spherical Tokamak for Energy Production (STEP)
The £220 million STEP programme aims to accelerate the delivery of fusion power to the energy market. STEP will be a prototype powerplant capable of demonstrating fusion as a viable technology for electricity generation. It uses the compact 'spherical tokamak' concept developed by UKAEA at Culham Centre for Fusion Energy. STEP is currently in a five-year conceptual design phase and is expected to be constructed and operational by 2040.
H3AT and FTF
In December 2017, UKAEA announced plans for two further fusion research centres: Hydrogen-3 Advanced Technology (H3AT) and Fusion Technology Facilities. H3AT, located at Culham, will study the processing and storage of tritium, one of the two fuels expected to supply commercial fusion reactors. The Fusion Technology Facilities, based at both Culham and at a new UKAEA Yorkshire site in Rotherham, South Yorkshire, carries out thermal, mechanical, hydraulic and electromagnetic tests on prototype components to replicate the conditions experienced inside fusion reactors.
Coat of arms
Locations
Authority site locations:
Culham Science Centre, Culham, Oxfordshire
Harwell Science and Innovation Campus, Oxfordshire
Advanced Manufacturing Park, Rotherham
Historical site locations:
Atomic Weapons Establishment, Aldermaston, Berkshire
Capenhurst (near Chester)
Chapelcross nuclear power station, Chapelcross (near Annan, Dumfries and Galloway)
Culcheth (near Warrington)
Daresbury Laboratory, Daresbury (near Warrington)
Dounreay, Caithness
Windscale (now part of Sellafield)
Risley (near Warrington)
Springfields (near Preston)
Winfrith, Dorset
See also
Atomic Energy Authority Act
Atomic Energy Research Establishment
Atomic Weapons Research Establishment
Nuclear weapons and the United Kingdom
BNFL
John Dolphin CBE
Nuclear Decommissioning Authority
Nuclear power in the United Kingdom
UK Atomic Energy Authority Constabulary
Campaign for Nuclear Disarmament
United States Atomic Energy Commission
References
External links
Culham Centre for Fusion Energy website
Dounreay Site Restoration Limited (DSRL) Website
Research Sites Restoration Limited (RSRL) Website
UKAEA History – The First Fifty Years
Harry Cartwright - Daily Telegraph obituary
Department for Business, Energy and Industrial Strategy
Government agencies established in 1954
Governmental nuclear organizations
1954 establishments in the United Kingdom
1954 in technology
1954 in the environment
Non-departmental public bodies of the United Kingdom government
Organisations based in Oxfordshire
Science and technology in Oxfordshire
Scientific organizations established in 1954 | United Kingdom Atomic Energy Authority | [
"Engineering"
] | 2,394 | [
"Governmental nuclear organizations",
"Nuclear organizations"
] |
601,070 | https://en.wikipedia.org/wiki/List%20of%20inequalities | This article lists Wikipedia articles about named mathematical inequalities.
Inequalities in pure mathematics
Analysis
Agmon's inequality
Askey–Gasper inequality
Babenko–Beckner inequality
Bernoulli's inequality
Bernstein's inequality (mathematical analysis)
Bessel's inequality
Bihari–LaSalle inequality
Bohnenblust–Hille inequality
Borell–Brascamp–Lieb inequality
Brezis–Gallouet inequality
Carleman's inequality
Chebyshev–Markov–Stieltjes inequalities
Chebyshev's sum inequality
Clarkson's inequalities
Eilenberg's inequality
Fekete–Szegő inequality
Fenchel's inequality
Friedrichs's inequality
Gagliardo–Nirenberg interpolation inequality
Gårding's inequality
Grothendieck inequality
Grunsky's inequalities
Hanner's inequalities
Hardy's inequality
Hardy–Littlewood inequality
Hardy–Littlewood–Sobolev inequality
Harnack's inequality
Hausdorff–Young inequality
Hermite–Hadamard inequality
Hilbert's inequality
Hölder's inequality
Jackson's inequality
Jensen's inequality
Khabibullin's conjecture on integral inequalities
Kantorovich inequality
Karamata's inequality
Korn's inequality
Ladyzhenskaya's inequality
Landau–Kolmogorov inequality
Lebedev–Milin inequality
Lieb–Thirring inequality
Littlewood's 4/3 inequality
Markov brothers' inequality
Mashreghi–Ransford inequality
Max–min inequality
Minkowski's inequality
Poincaré inequality
Popoviciu's inequality
Prékopa–Leindler inequality
Rayleigh–Faber–Krahn inequality
Remez inequality
Riesz rearrangement inequality
Schur test
Shapiro inequality
Sobolev inequality
Steffensen's inequality
Szegő inequality
Three spheres inequality
Trace inequalities
Trudinger's theorem
Turán's inequalities
Von Neumann's inequality
Wirtinger's inequality for functions
Young's convolution inequality
Young's inequality for products
Inequalities relating to means
Hardy–Littlewood maximal inequality
Inequality of arithmetic and geometric means
Ky Fan inequality
Levinson's inequality
Maclaurin's inequality
Mahler's inequality
Muirhead's inequality
Newton's inequalities
Stein–Strömberg theorem
Combinatorics
Binomial coefficient bounds
Factorial bounds
XYZ inequality
Fisher's inequality
Ingleton's inequality
Lubell–Yamamoto–Meshalkin inequality
Nesbitt's inequality
Rearrangement inequality
Schur's inequality
Shapiro inequality
Stirling's formula (bounds)
Differential equations
Grönwall's inequality
Geometry
Alexandrov–Fenchel inequality
Aristarchus's inequality
Barrow's inequality
Berger–Kazdan comparison theorem
Blaschke–Lebesgue inequality
Blaschke–Santaló inequality
Bishop–Gromov inequality
Bogomolov–Miyaoka–Yau inequality
Bonnesen's inequality
Brascamp–Lieb inequality
Brunn–Minkowski inequality
Castelnuovo–Severi inequality
Cheng's eigenvalue comparison theorem
Clifford's theorem on special divisors
Cohn-Vossen's inequality
Erdős–Mordell inequality
Euler's theorem in geometry
Gromov's inequality for complex projective space
Gromov's systolic inequality for essential manifolds
Hadamard's inequality
Hadwiger–Finsler inequality
Hinge theorem
Hitchin–Thorpe inequality
Isoperimetric inequality
Jordan's inequality
Jung's theorem
Loewner's torus inequality
Łojasiewicz inequality
Loomis–Whitney inequality
Melchior's inequality
Milman's reverse Brunn–Minkowski inequality
Milnor–Wood inequality
Minkowski's first inequality for convex bodies
Myers's theorem
Noether inequality
Ono's inequality
Pedoe's inequality
Ptolemy's inequality
Pu's inequality
Riemannian Penrose inequality
Toponogov's theorem
Triangle inequality
Weitzenböck's inequality
Wirtinger inequality (2-forms)
Information theory
Inequalities in information theory
Kraft's inequality
Log sum inequality
Welch bounds
Algebra
Abhyankar's inequality
Pisier–Ringrose inequality
Linear algebra
Abel's inequality
Bregman–Minc inequality
Cauchy–Schwarz inequality
Golden–Thompson inequality
Hadamard's inequality
Hoffman-Wielandt inequality
Peetre's inequality
Sylvester's rank inequality
Triangle inequality
Trace inequalities
Eigenvalue inequalities
Bendixson's inequality
Weyl's inequality in matrix theory
Cauchy interlacing theorem
Poincaré separation theorem
Number theory
Bonse's inequality
Large sieve inequality
Pólya–Vinogradov inequality
Turán–Kubilius inequality
Weyl's inequality
Probability theory and statistics
Azuma's inequality
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount
Bhatia–Davis inequality, an upper bound on the variance of any bounded probability distribution
Bernstein inequalities (probability theory)
Boole's inequality
Borell–TIS inequality
BRS-inequality
Burkholder's inequality
Burkholder–Davis–Gundy inequalities
Cantelli's inequality
Chebyshev's inequality
Chernoff's inequality
Chung–Erdős inequality
Concentration inequality
Cramér–Rao inequality
Doob's martingale inequality
Dvoretzky–Kiefer–Wolfowitz inequality
Eaton's inequality, a bound on the largest absolute value of a linear combination of bounded random variables
Emery's inequality
Entropy power inequality
Etemadi's inequality
Fannes–Audenaert inequality
Fano's inequality
Fefferman's inequality
Fréchet inequalities
Gauss's inequality
Gauss–Markov theorem, the statement that the least-squares estimators in certain linear models are the best linear unbiased estimators
Gaussian correlation inequality
Gaussian isoperimetric inequality
Gibbs's inequality
Hoeffding's inequality
Hoeffding's lemma
Jensen's inequality
Khintchine inequality
Kolmogorov's inequality
Kunita–Watanabe inequality
Le Cam's theorem
Lenglart's inequality
Marcinkiewicz–Zygmund inequality
Markov's inequality
McDiarmid's inequality
Paley–Zygmund inequality
Pinsker's inequality
Popoviciu's inequality on variances
Prophet inequality
Rao–Blackwell theorem
Ross's conjecture, a lower bound on the average waiting time in certain queues
Samuelson's inequality
Shearer's inequality
Stochastic Gronwall inequality
Talagrand's concentration inequality
Vitale's random Brunn–Minkowski inequality
Vysochanskiï–Petunin inequality
Topology
Berger's inequality for Einstein manifolds
Inequalities particular to physics
Ahlswede–Daykin inequality
Bell's inequality – see Bell's theorem
Bell's original inequality
CHSH inequality
Clausius–Duhem inequality
Correlation inequality – any of several inequalities
FKG inequality
Ginibre inequality
Griffiths inequality
Heisenberg's inequality
Holley inequality
Leggett–Garg inequality
Riemannian Penrose inequality
Rushbrooke inequality
Tsirelson's inequality
See also
Comparison theorem
List of mathematical identities
Lists of mathematics topics
List of set identities and relations
Inequalities | List of inequalities | [
"Mathematics"
] | 1,542 | [
"Binary relations",
"Mathematical relations",
"Inequalities (mathematics)",
"Mathematical problems",
"Mathematical theorems"
] |
601,086 | https://en.wikipedia.org/wiki/Rarefaction | Rarefaction is the reduction of an item's density, the opposite of compression. Like compression, which can travel in waves (sound waves, for instance), rarefaction waves also exist in nature. A common rarefaction wave is the area of low relative pressure following a shock wave (see picture).
Rarefaction waves expand with time (much like sea waves spread out as they reach a beach); in most cases rarefaction waves keep the same overall profile ('shape') at all times throughout the wave's movement: it is a self-similar expansion. Each part of the wave travels at the local speed of sound, in the local medium. This expansion behaviour contrasts with that of pressure increases, which gets narrower with time until they steepen into shock waves.
Physical examples
A natural example of rarefaction occurs in the layers of Earth's atmosphere. Because the atmosphere has mass, most atmospheric matter is nearer to the Earth due to the Earth's gravitation. Therefore, air at higher layers of the atmosphere is less dense, or rarefied, relative to air at lower layers. Thus, rarefaction can refer either to a reduction in density over space at a single point of time, or a reduction of density over time for one particular area.
Rarefaction can be easily observed by compressing a spring and releasing it.
In manufacturing
Modern construction of guitars is an example of using rarefaction in manufacturing. By forcing the reduction of density (loss of oils and other impurities) in the cellular structure of the soundboard, a rarefied guitar top produces a tonal decompression affecting the sound of the instrument, mimicking aged wood.
See also
Longitudinal wave
P-wave
Prandtl–Meyer expansion fan
Rarefied gas dynamics
Citations
Sound
Acoustics
Waves
Conservation equations | Rarefaction | [
"Physics",
"Mathematics"
] | 372 | [
"Physical phenomena",
"Conservation laws",
"Mathematical objects",
"Classical mechanics",
"Acoustics",
"Equations",
"Waves",
"Motion (physics)",
"Conservation equations",
"Symmetry",
"Physics theorems"
] |
601,240 | https://en.wikipedia.org/wiki/Semantic%20theory%20of%20truth | A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.
Origin
The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work by Polish logician Alfred Tarski. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the liar paradox. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique Kurt Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot be defined within that language.
Tarski's theory of truth
To formulate linguistic theories without semantic paradoxes such as the liar paradox, it is generally necessary to distinguish the language that one is talking about (the object language) from the language that one is using to do the talking (the metalanguage). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "P") is always the metalanguage's name for a sentence, such that this name is simply the sentence P rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski's theory of truth (Alfred Tarski 1935) demanded that the object language be contained in the metalanguage.
Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "P", a sentence of the following form (known as "form (T)"):
(1) "P" is true if, and only if, P.
For example,
(2) 'snow is white' is true if and only if snow is white.
These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both English; here is an example where the object language is German and the metalanguage is English:
(3) 'Schnee ist weiß' is true if and only if snow is white.
It is important to note that as Tarski originally formulated it, this theory applies only to formal languages, cf. also semantics of first-order logic. He gave a number of reasons for not extending his theory to natural languages, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is closed (that is, it can describe the semantic characteristics of its own elements). But Tarski's approach was extended by Davidson into an approach to theories of meaning for natural languages, which involves treating "truth" as a primitive, rather than a defined, concept. (See truth-conditional semantics.)
Tarski developed the theory to give an inductive definition of truth as follows. (See T-schema)
For a language L containing ¬ ("not"), ∧ ("and"), ∨ ("or"), ∀ ("for all"), and ∃ ("there exists"), Tarski's inductive definition of truth looks like this:
(1) A primitive statement "A" is true if, and only if, A.
(2) "¬A" is true if, and only if, "A" is not true.
(3) "A∧B" is true if, and only if, "A" is true and "B" is true.
(4) "A∨B" is true if, and only if, "A" is true or "B" is true or ("A" is true and "B" is true).
(5) "∀x(Fx)" is true if, and only if, for all objects x, "Fx" is true.
(6) "∃x(Fx)" is true if, and only if, there is an object x for which "Fx" is true.
These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents. The simplest constituents are atomic sentences. A contemporary semantic definition of truth would define truth for the atomic sentences as follows:
An atomic sentence F(x1,...,xn) is true (relative to an assignment of values to the variables x1, ..., xn)) if the corresponding values of variables bear the relation expressed by the predicate F.
Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in the context of truth. Therefore it would be circular to use one of them in the definition of truth itself. Tarski's semantic conception of truth plays an important role in modern logic and also in contemporary philosophy of language. It is a rather controversial point whether Tarski's semantic theory should be counted either as a correspondence theory or as a deflationary theory.
Kripke's theory of truth
Kripke's theory of truth (Saul Kripke 1975) is based on partial logic (a logic of partially defined truth predicates instead of Tarski's logic of totally defined truth predicates) with the strong Kleene evaluation scheme.
See also
Disquotational principle
Semantics of logic
T-schema
Triune continuum paradigm
References
Further reading
Simon Blackburn and Keith Simmons, eds., 1999. Truth. Oxford University Press, .
Michael K Butler, 2017. Deflationism and Semantic Theories of Truth. Pendlebury Press, .
Wilfrid Hodges, 2001. Tarski's truth definitions. In the Stanford Encyclopedia of Philosophy.
Richard Kirkham, 1992. Theories of Truth. Bradford Books, .
Saul Kripke, 1975. "Outline of a Theory of Truth". Journal of Philosophy, 72: 690–716.
Alfred Tarski, 1935. "The Concept of Truth in Formalized Languages". Logic, Semantics, Metamathematics, Indianapolis: Hackett 1983, 2nd edition, 152–278.
Alfred Tarski, 1944. The Semantic Conception of Truth and the Foundations of Semantics. Philosophy and Phenomenological Research 4.
External links
Semantic Theory of Truth, Internet Encyclopedia of Philosophy
Tarski's Truth Definitions (an entry of Stanford Encyclopedia of Philosophy)
Alfred Tarski, 1944. The Semantic Conception of Truth and the Foundations of Semantics. Philosophy and Phenomenological Research 4.
Mathematical logic
Semantics
Theories of truth
Theories of deduction | Semantic theory of truth | [
"Mathematics"
] | 1,433 | [
"Mathematical logic",
"Theories of deduction"
] |
601,254 | https://en.wikipedia.org/wiki/Tritonal | Tritonal is a mixture of 80% TNT and 20% aluminium powder, used in several types of ordnance such as air-dropped bombs. The aluminium increases the total heat output and hence impulse of the TNT – the length of time during which the blast wave is positive. Tritonal is approximately 18% more powerful than TNT alone.
The 87 kg of tritonal in a Mark 82 bomb has the potential to produce approximately 863 MJ of energy when detonated. This implies a specific energy of approximately 9 MJ/kg, compared to ~4 MJ/kg for TNT.
History
TNT was first prepared by Julius Wilbrand in 1863. Germany began manufacturing TNT in 1891 and aluminium was first mixed with TNT in 1899 to produce an explosive compound. In 1902, the German Army began to use TNT, replacing picric acid, and in 1912, the US Army also started to use TNT. TNT production was limited by the availability of toluene which came from coal tar. Therefore, mixtures of TNT with other compounds became widespread to relieve the shortage of TNT.
Modern tritonal was developed as a cheaper substitute for Torpex and HBX under UWE designation (UnderWater Explosive) before it turned out Allies could produce enough RDX to cover all naval requirements late in WWII.
See also
Torpex
Composition H6
Minol
Relative effectiveness factor (RE)
References
Explosives
Trinitrotoluene | Tritonal | [
"Chemistry"
] | 287 | [
"Explosive chemicals",
"Trinitrotoluene",
"Explosives",
"Explosions"
] |
601,284 | https://en.wikipedia.org/wiki/Paul%20Erd%C5%91s | Paul Erdős (, ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered on discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed.
He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle; Time magazine called him "The Oddball's Oddball". He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. He devoted his waking hours to mathematics, even into his later years; he died at a mathematics conference in Warsaw in 1996.
Erdős's prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships.
Life
Paul Erdős was born on 26 March 1913, in Budapest, Austria-Hungary, the only surviving child of Anna (née Wilhelm) and Lajos Erdős (né Engländer). His two sisters, aged three and five, both died of scarlet fever a few days before he was born. His parents, both Jewish, were high school mathematics teachers. His fascination with mathematics developed early. He was raised partly by a German governess because his father was held captive in Siberia as an Austro-Hungarian prisoner of war during 1914–1920, causing his mother to have to work long hours to support their household. His father had taught himself English while in captivity, but mispronounced many words. When Lajos later taught his son to speak English, Paul learned his father's pronunciation, which he continued to use for the rest of his life.
He taught himself to read through mathematics texts that his parents left around in their home. By the age of five, given a person's age, he could calculate in his head how many seconds they had lived. Due to his sisters' deaths, he had a close relationship with his mother, with the two of them reportedly sharing the same bed until he left for college.
When he was 16, his father introduced him to two subjects that would become lifetime favourites—infinite series and set theory. In high school, Erdős became an ardent solver of the problems that appeared each month in KöMaL, the "Mathematical and Physical Journal for Secondary Schools".
Erdős began studying at the University of Budapest when he was 17 after winning a national examination. At the time, admission of Jews to Hungarian universities was severely restricted under the numerus clausus. By the time he was 20, he had found a proof for Chebyshev's theorem. In 1934, at the age of 21, he was awarded a doctorate in mathematics. Erdős's thesis advisor was Lipót Fejér, who was also the thesis advisor for John von Neumann, George Pólya, and Paul (Pál) Turán. He took up a post-doctoral fellowship at Manchester, as Jews in Hungary were suffering oppression under the authoritarian regime. While there he met Godfrey Harold Hardy and Stan Ulam.
Because he was Jewish, Erdős decided Hungary was dangerous and left the country, relocating to the United States in 1938. Many members of Erdős's family, including two of his aunts, two of his uncles, and his father, died in Budapest during World War II. His mother was the only one that survived. He was living in America and working at the Institute for Advanced Study in Princeton at the time. However, his fellowship at Princeton only got extended by 6 months rather than the expected year due to Erdős not conforming to the standards of the place; they found him "uncouth and unconventional".
Described by his biographer, Paul Hoffman, as "probably the most eccentric mathematician in the world," Erdős spent most of his adult life living out of a suitcase. Except for some years in the 1950s, when he was not allowed to enter the United States based on the accusation that he was a Communist sympathizer, his life was a continuous series of going from one meeting or seminar to another. During his visits, Erdős expected his hosts to lodge him, feed him, and do his laundry, along with anything else he needed, as well as arrange for him to get to his next destination.
Ulam left his post at the University of Wisconsin–Madison in 1943 to work on the Manhattan Project in Los Alamos, New Mexico with other mathematicians and physicists. He invited Erdős to join the project, but the invitation was withdrawn when Erdős expressed a desire to return to Hungary after the war.
On 20 September 1996, at the age of 83, he had a heart attack and died while attending a conference in Warsaw. These circumstances were close to the way he wanted to die. He once said,
Erdős never married and had no children. He is buried next to his mother and father in the Jewish Kozma Street Cemetery in Budapest. For his epitaph, he suggested "I've finally stopped getting dumber." (Hungarian: "Végre nem butulok tovább").
Erdős's name contains the Hungarian letter "ő" ("o" with double acute accent), but is often incorrectly written as Erdos or Erdös either "by mistake or out of typographical necessity".
Career
In 1934, Erdős moved to Manchester, England, to be a guest lecturer. In 1938, he accepted his first American position as a scholarship holder at the Institute for Advanced Study, Princeton, New Jersey, for the next ten years. Despite outstanding papers with Mark Kac and Aurel Wintner on probabilistic number theory, Pál Turán in approximation theory, and Witold Hurewicz on dimension theory, his fellowship was not continued, and
Erdős was forced to take positions as a wandering scholar at UPenn, Notre Dame, Purdue, Stanford, and Syracuse. He would not stay long in one place, instead traveling among mathematical institutions until his death.
As a result of the Red Scare and McCarthyism, in 1954, the Immigration and Naturalization Service denied Erdős, a Hungarian citizen, a re-entry visa into the United States. Teaching at the University of Notre Dame at the time, Erdős could have chosen to remain in the country. Instead, he packed up and left, albeit requesting reconsideration from the U.S. Immigration Services at periodic intervals. At some point he moved to live in Israel, and was given a position for three months at the Hebrew University in Jerusalem, and then a "permanent visiting professor" position at the Technion.
Hungary at the time was under the Warsaw Pact with the Soviet Union. Although Hungary limited the freedom of its own citizens to enter and exit the country, in 1956 it gave Erdős the exclusive privilege of being allowed to enter and exit the country as he pleased.
In 1963, the U.S. Immigration Service granted Erdős a visa, and he resumed teaching at and traveling to American institutions. Ten years later, in 1973, the 60-year-old Erdős voluntarily left Hungary.
During the last decades of his life, Erdős received at least fifteen honorary doctorates. He became a member of the scientific academies of eight countries, including the U.S. National Academy of Sciences and the UK Royal Society. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1977. Shortly before his death, he renounced his honorary degree from the University of Waterloo over what he considered to be unfair treatment of colleague Adrian Bondy.
Mathematical work
Erdős was one of the most prolific publishers of papers in mathematical history, comparable only with Leonhard Euler; Erdős published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself. Erdős wrote around 1,525 mathematical articles in his lifetime, mostly with co-authors. He strongly believed in and practiced mathematics as a social activity, having 511 different collaborators in his lifetime.
In his mathematical style, Erdős was much more of a "problem solver" than a "theory developer" (see "The Two Cultures of Mathematics" by Timothy Gowers for an in-depth discussion of the two styles, and why problem solvers are perhaps less appreciated). Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career." Erdős never won the Fields Medal (the highest mathematical prize available during his lifetime), nor did he coauthor a paper with anyone who did, a pattern that extends to other prizes. He did win the 1983/84 Wolf Prize, "for his numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for personally stimulating mathematicians the world over". In contrast, the works of the three winners after were recognized as "outstanding", "classic", and "profound", and the three before as "fundamental" or "seminal".
Of his contributions, the development of Ramsey theory and the application of the probabilistic method especially stand out. Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory. Erdős found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original one. He also discovered the first elementary proof for the prime number theorem, along with Atle Selberg. However, the circumstances leading up to the proofs, as well as publication disagreements, led to a bitter dispute between Erdős and Selberg. Erdős also contributed to fields in which he had little real interest, such as topology, where he is credited as the first person to give an example of a totally disconnected topological space that is not zero-dimensional, the Erdős space.
Erdős's problems
Erdős had a reputation for posing new problems as well as solving existing ones – Ernst Strauss called him "the absolute monarch of problem posers". Throughout his career, Erdős would offer payments for solutions to unresolved problems. These ranged from $25 for problems that he felt were just out of the reach of the current mathematical thinking (both his and others) up to $10,000 for problems that were both difficult to attack and mathematically significant. Some of these problems have since been solved, including the most lucrative – Erdős's conjecture on prime gaps was solved in 2014, and the $10,000 paid.
There are thought to be at least a thousand remaining unsolved problems, though there is no official or comprehensive list. The offers remained active despite Erdős's death; Ronald Graham was the (informal) administrator of solutions, and a solver could receive either an original check signed by Erdős before his death (for memento only, cannot be cashed) or a cashable check from Graham. British mathematician Thomas Bloom started a website dedicated to Erdős's problems in 2024.
Perhaps the most mathematically notable of these problems is the Erdős conjecture on arithmetic progressions:
If true, it would solve several other open problems in number theory (although one main implication of the conjecture, that the prime numbers contain arbitrarily long arithmetic progressions, has since been proved independently as the Green–Tao theorem). The payment for the solution of the problem is currently worth US$5,000.
The most familiar problem with an Erdős prize is likely the Collatz conjecture, also called the 3N + 1 problem. Erdős offered $500 for a solution.
Collaborators
Erdős' most frequent collaborators include Hungarian mathematicians András Sárközy (62 papers) and András Hajnal (56 papers), and American mathematician Ralph Faudree (50 papers). Other frequent collaborators were the following:
Richard Schelp (42 papers)
C. C. Rousseau (35 papers)
Vera Sós (35 papers)
Alfréd Rényi (32 papers)
Pál Turán (30 papers)
Endre Szemerédi (29 papers)
Ron Graham (28 papers)
Stefan Burr (27 papers)
Carl Pomerance (23 papers)
Joel Spencer (23 papers)
János Pach (21 papers)
Miklós Simonovits (21 papers)
Ernst G. Straus (20 papers)
Melvyn B. Nathanson (19 papers)
Jean-Louis Nicolas (19 papers)
Richard Rado (18 papers)
Béla Bollobás (18 papers)
Eric Charles Milner (15 papers)
András Gyárfás (15 papers)
John Selfridge (14 papers)
Fan Chung (14 papers)
Richard R. Hall (14 papers)
George Piranian (14 papers)
István Joó (12 papers)
Zsolt Tuza (12 papers)
A. R. Reddy (11 papers)
Vojtěch Rödl (11 papers)
Pál Révész (10 papers)
Zoltán Füredi (10 papers)
For other co-authors of Erdős, see the list of people with Erdős number 1 in List of people by Erdős number.
Erdős number
Because of his prolific output, friends created the Erdős number as a tribute. An Erdős number describes a person's degree of separation from Erdős himself, based on their collaboration with him, or with another who has their own Erdős number. Erdős alone was assigned the Erdős number of 0 (for being himself), while his immediate collaborators could claim an Erdős number of 1, their collaborators have Erdős number at most 2, and so on. Approximately 200,000 mathematicians have an assigned Erdős number, and some have estimated that 90 percent of the world's active mathematicians have an Erdős number smaller than 8 (not surprising in light of the small-world phenomenon). Due to collaborations with mathematicians, many scientists in fields such as physics, engineering, biology, and economics also have Erdős numbers.
Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers. For example, the roughly 268,000 mathematicians with a known Erdős number have a median value of 5. In contrast, the median Erdős number of Fields Medalists is 3. As of 2015, approximately 11,000 mathematicians have an Erdős number of 2 or less. Collaboration distances will necessarily increase over long time scales, as mathematicians with low Erdős numbers die and become unavailable for collaboration. The American Mathematical Society provides a free online tool to determine the Erdős number of every mathematical author listed in the Mathematical Reviews catalogue.
The Erdős number was most likely first defined by Casper Goffman, an analyst whose own Erdős number is 2; Goffman co-authored with mathematician Richard B. Darst, who co-authored with Erdős. Goffman published his observations about Erdős's prolific collaboration in a 1969 article titled "And what is your Erdős number?"
Jerry Grossman has written that it could be argued that Baseball Hall of Famer Hank Aaron can be considered to have an Erdős number of 1 because they both autographed the same baseball (for Carl Pomerance) when Emory University awarded them honorary degrees on the same day. Erdős numbers have also been proposed for an infant, a horse, and several actors.
Personality
Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life traveling between scientific conferences, universities and the homes of colleagues all over the world. He earned enough in stipends from universities as a guest lecturer, and from various mathematical awards, to fund his travels and basic needs; money left over he used to fund cash prizes for proofs of "Erdős's problems" (see above). He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom to visit next.
His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems", and Erdős drank copious quantities; this quotation is often attributed incorrectly to Erdős, but Erdős himself ascribed it to Rényi. After his mother's death in 1971 he started taking antidepressants and amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking them for a month. Erdős won the bet, but complained that it impacted his performance: "You've showed me I'm not an addict. But I didn't get any work done. I'd get up in the morning and stare at a blank piece of paper. I'd have no ideas, just like an ordinary person. You've set mathematics back a month." After he won the bet, he promptly resumed his use of Ritalin and Benzedrine.
He had his own idiosyncratic vocabulary; although an agnostic atheist, he spoke of "The Book", a visualization of a book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God. He playfully nicknamed him the SF (for "Supreme Fascist"), accusing him of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from The Book!" This later inspired a book titled Proofs from the Book.
Other idiosyncratic elements of Erdős's vocabulary include:
Children were referred to as "epsilons" (because in mathematics, particularly calculus, an arbitrarily small positive quantity is commonly denoted by the Greek letter (ε)).
Women were "bosses" who "captured" men as "slaves" by marrying them. Divorced men were "liberated".
People who stopped doing mathematics had "died", while people who died had "left".
Alcoholic drinks were "poison".
Music (except classical music) was "noise".
To be considered a hack was to be a "Newton".
To give a mathematical lecture was "to preach".
Mathematical lectures themselves were "sermons".
To give an oral exam to students was "to torture" them.
He gave nicknames to many countries, examples being: the U.S. was "samland" (after Uncle Sam) and the Soviet Union was "joedom" (after Joseph Stalin). He claimed that Hindi was the best language because words for old age (bud̩d̩hā) and stupidity (buddhū) sounded almost the same.
Signature
Erdős signed his name "Paul Erdos P.G.O.M." When he became 60, he added "L.D.", at 65 "A.D.", at 70 "L.D." (again), and at 75 "C.D."
P.G.O.M. represented "Poor Great Old Man"
The first L.D. represented "Living Dead"
A.D. represented "Archaeological Discovery"
The second L.D. represented "Legally Dead"
C.D. represented "Counts Dead"
Legacy
Books and films
Erdős is the subject of at least three books: two biographies (Hoffman's The Man Who Loved Only Numbers and Schechter's My Brain is Open, both published in 1998) and a 2013 children's picture book by Deborah Heiligman (The Boy Who Loved Math: The Improbable Life of Paul Erdős).
He is also the subject of George Csicsery's biographical documentary film N is a Number: A Portrait of Paul Erdős, made while he was still alive.
Astronomy
In 2021 the minor planet (asteroid) 405571 (temporarily designated 2005 QE87) was formally named "Erdőspál" to commemorate Erdős, with the citation describing him as "a Hungarian mathematician, much of whose work centered around discrete mathematics. His work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics." The naming was proposed by "K. Sárneczky, Z. Kuli" (Kuli being the asteroid's discoverer).
See also
– including conjectures, numbers, prizes, and theorems
References
Sources
Further reading
External links
Searchable collection of (almost) all papers of Erdős
Database of problems proposed by Erdős
The Erdös Number Project at Oakland University
The Man Who Loved Only Numbers, public lecture by Paul Hoffman
"Open problems of Paul Erdős in graph theory" by Fan Chung
1913 births
1996 deaths
20th-century Hungarian Jews
20th-century Hungarian mathematicians
Academics of the Victoria University of Manchester
Burials at Kozma Street Cemetery
Combinatorialists
Eötvös Loránd University alumni
Foreign associates of the National Academy of Sciences
Foreign members of the Royal Society
Graph theorists
Hungarian agnostics
Hungarian atheists
Institute for Advanced Study visiting scholars
Jewish agnostics
Jewish atheists
Mathematicians at the University of Pennsylvania
Mathematicians from Austria-Hungary
Mathematicians from Budapest
Members of the Hungarian Academy of Sciences
Members of the Royal Netherlands Academy of Arts and Sciences
Mental calculators
Network scientists
Number theorists
Princeton University faculty
Probability theorists
Purdue University faculty
Set theorists
Stanford University faculty
Syracuse University faculty
University of Notre Dame faculty
University of Pennsylvania faculty
Wolf Prize in Mathematics laureates | Paul Erdős | [
"Mathematics"
] | 4,539 | [
"Graph theory",
"Combinatorics",
"Number theorists",
"Mathematical relations",
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"Graph theorists",
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601,399 | https://en.wikipedia.org/wiki/Display%20resolution | The display resolution or display modes of a digital television, computer monitor, or other display device is the number of distinct pixels in each dimension that can be displayed. It can be an ambiguous term especially as the displayed resolution is controlled by different factors in cathode-ray tube (CRT) displays, flat-panel displays (including liquid-crystal displays) and projection displays using fixed picture-element (pixel) arrays.
It is usually quoted as , with the units in pixels: for example, means the width is 1024 pixels and the height is 768 pixels. This example would normally be spoken as "ten twenty-four by seven sixty-eight" or "ten twenty-four by seven six eight".
One use of the term display resolution applies to fixed-pixel-array displays such as plasma display panels (PDP), liquid-crystal displays (LCD), Digital Light Processing (DLP) projectors, OLED displays, and similar technologies, and is simply the physical number of columns and rows of pixels creating the display (e.g. ). A consequence of having a fixed-grid display is that, for multi-format video inputs, all displays need a "scaling engine" (a digital video processor that includes a memory array) to match the incoming picture format to the display.
For device displays such as phones, tablets, monitors and televisions, the use of the term display resolution as defined above is a misnomer, though common. The term display resolution is usually used to mean pixel dimensions, the maximum number of pixels in each dimension (e.g. ), which does not tell anything about the pixel density of the display on which the image is actually formed: resolution properly refers to the pixel density, the number of pixels per unit distance or area, not the total number of pixels. In digital measurement, the display resolution would be given in pixels per inch (PPI). In analog measurement, if the screen is 10 inches high, then the horizontal resolution is measured across a square 10 inches wide. For television standards, this is typically stated as "lines horizontal resolution, per picture height"; for example, analog NTSC TVs can typically display about 340 lines of "per picture height" horizontal resolution from over-the-air sources, which is equivalent to about 440 total lines of actual picture information from left edge to right edge.
Background
Some commentators also use display resolution to indicate a range of input formats that the display's input electronics will accept and often include formats greater than the screen's native grid size even though they have to be down-scaled to match the screen's parameters (e.g. accepting a input on a display with a native pixel array). In the case of television inputs, many manufacturers will take the input and zoom it out to "overscan" the display by as much as 5% so input resolution is not necessarily display resolution.
The eye's perception of display resolution can be affected by a number of factors see image resolution and optical resolution. One factor is the display screen's rectangular shape, which is expressed as the ratio of the physical picture width to the physical picture height. This is known as the aspect ratio. A screen's physical aspect ratio and the individual pixels' aspect ratio may not necessarily be the same. An array of on a 16:9 display has square pixels, but an array of on a 16:9 display has oblong pixels.
An example of pixel shape affecting "resolution" or perceived sharpness: displaying more information in a smaller area using a higher resolution makes the image much clearer or "sharper". However, most recent screen technologies are fixed at a certain resolution; making the resolution lower on these kinds of screens will greatly decrease sharpness, as an interpolation process is used to "fix" the non-native resolution input into the display's native resolution output.
While some CRT-based displays may use digital video processing that involves image scaling using memory arrays, ultimately "display resolution" in CRT-type displays is affected by different parameters such as spot size and focus, astigmatic effects in the display corners, the color phosphor pitch shadow mask (such as Trinitron) in color displays, and the video bandwidth.
Aspects
Overscan and underscan
Most television display manufacturers "overscan" the pictures on their displays (CRTs and PDPs, LCDs etc.), so that the effective on-screen picture may be reduced from (480) to (450), for example. The size of the invisible area somewhat depends on the display device. Some HD televisions do this as well, to a similar extent.
Computer displays including projectors generally do not overscan although many models (particularly CRT displays) allow it. CRT displays tend to be underscanned in stock configurations, to compensate for the increasing distortions at the corners.
Interlaced versus progressive scan
Interlaced video (also known as interlaced scan) is a technique for doubling the perceived frame rate of a video display without consuming extra bandwidth. The interlaced signal contains two fields of a video frame captured consecutively. This enhances motion perception to the viewer, and reduces flicker by taking advantage of the phi phenomenon.
The European Broadcasting Union has argued against interlaced video in production and broadcasting. The main argument is that no matter how complex the deinterlacing algorithm may be, the artifacts in the interlaced signal cannot be completely eliminated because some information is lost between frames. Despite arguments against it, television standards organizations continue to support interlacing. It is still included in digital video transmission formats such as DV, DVB, and ATSC. New video compression standards like High Efficiency Video Coding are optimized for progressive scan video, but sometimes do support interlaced video.
Progressive scanning (alternatively referred to as noninterlaced scanning) is a format of displaying, storing, or transmitting moving images in which all the lines of each frame are drawn in sequence. This is in contrast to interlaced video used in traditional analog television systems where only the odd lines, then the even lines of each frame (each image called a video field) are drawn alternately, so that only half the number of actual image frames are used to produce video.
Televisions
Current standards
Televisions are of the following resolutions:
Standard-definition television (SDTV):
480i (NTSC-compatible digital standard employing two interlaced fields of 240 lines each)
576i (PAL-compatible digital standard employing two interlaced fields of 288 lines each)
Enhanced-definition television (EDTV):
480p ( progressive scan)
576p ( progressive scan)
High-definition television (HDTV):
720p ( progressive scan)
1080i ( split into two interlaced fields of 540 lines)
1080p ( progressive scan)
Ultra-high-definition television (UHDTV):
4K UHD ( progressive scan)
8K UHD ( progressive scan)
Film industry
As far as digital cinematography is concerned, video resolution standards depend first on the frames' aspect ratio in the film stock (which is usually scanned for digital intermediate post-production) and then on the actual points' count. Although there is not a unique set of standardized sizes, it is commonplace within the motion picture industry to refer to "nK" image "quality", where n is a (small, usually even) integer number which translates into a set of actual resolutions, depending on the film format. As a reference consider that, for a 4:3 (around 1.33:1) aspect ratio which a film frame (no matter what is its format) is expected to horizontally fit in, n is the multiplier of 1024 such that the horizontal resolution is exactly 1024•n points. For example, 2K reference resolution is pixels, whereas 4K reference resolution is pixels. Nevertheless, 2K may also refer to resolutions like (full-aperture), (HDTV, 16:9 aspect ratio) or pixels (Cinemascope, 2.35:1 aspect ratio). It is also worth noting that while a frame resolution may be, for example, 3:2 ( NTSC), that is not what you will see on-screen (i.e. 4:3 or 16:9 depending on the intended aspect ratio of the original material).
Computer monitors
Computer monitors have traditionally possessed higher resolutions than most televisions.
Evolution of standards
Many personal computers introduced in the late 1970s and the 1980s were designed to use television receivers as their display devices, making the resolutions dependent on the television standards in use, including PAL and NTSC. Picture sizes were usually limited to ensure the visibility of all the pixels in the major television standards and the broad range of television sets with varying amounts of over scan. The actual drawable picture area was, therefore, somewhat smaller than the whole screen, and was usually surrounded by a static-colored border (see image below). Also, the interlace scanning was usually omitted in order to provide more stability to the picture, effectively halving the vertical resolution in progress. , and on NTSC were relatively common resolutions in the era (224, 240 or 256 scanlines were also common). In the IBM PC world, these resolutions came to be used by 16-color EGA video cards.
One of the drawbacks of using a classic television is that the computer display resolution is higher than the television could decode. Chroma resolution for NTSC/PAL televisions are bandwidth-limited to a maximum 1.5MHz, or approximately 160 pixels wide, which led to blurring of the color for 320- or 640-wide signals, and made text difficult to read (see example image below). Many users upgraded to higher-quality televisions with S-Video or RGBI inputs that helped eliminate chroma blur and produce more legible displays. The earliest, lowest cost solution to the chroma problem was offered in the Atari 2600 Video Computer System and the Apple II+, both of which offered the option to disable the color and view a legacy black-and-white signal. On the Commodore 64, the GEOS mirrored the Mac OS method of using black-and-white to improve readability.
The resolution ( with borders disabled) was first introduced by home computers such as the Commodore Amiga and, later, Atari Falcon. These computers used interlace to boost the maximum vertical resolution. These modes were only suited to graphics or gaming, as the flickering interlace made reading text in word processor, database, or spreadsheet software difficult. (Modern game consoles solve this problem by pre-filtering the 480i video to a lower resolution. For example, Final Fantasy XII suffers from flicker when the filter is turned off, but stabilizes once filtering is restored. The computers of the 1980s lacked sufficient power to run similar filtering software.)
The advantage of a overscanned computer was an easy interface with interlaced TV production, leading to the development of Newtek's Video Toaster. This device allowed Amigas to be used for CGI creation in various news departments (example: weather overlays), drama programs such as NBC's seaQuest and The WB's Babylon 5.
In the PC world, the IBM PS/2 VGA (multi-color) on-board graphics chips used a non-interlaced (progressive) 640 × 480 × 16 color resolution that was easier to read and thus more useful for office work. It was the standard resolution from 1990 to around 1996. The standard resolution was until around 2000. Microsoft Windows XP, released in 2001, was designed to run at minimum, although it is possible to select the original in the Advanced Settings window.
Programs designed to mimic older hardware such as Atari, Sega, or Nintendo game consoles (emulators) when attached to multiscan CRTs, routinely use much lower resolutions, such as or for greater authenticity, though other emulators have taken advantage of pixelation recognition on circle, square, triangle and other geometric features on a lesser resolution for a more scaled vector rendering. Some emulators, at higher resolutions, can even mimic the aperture grille and shadow masks of CRT monitors.
In 2002, eXtended Graphics Array was the most common display resolution. Many web sites and multimedia products were re-designed from the previous format to the layouts optimized for .
The availability of inexpensive LCD monitors made the aspect ratio resolution of more popular for desktop usage during the first decade of the 21st century. Many computer users including CAD users, graphic artists and video game players ran their computers at resolution (UXGA) or higher such as QXGA if they had the necessary equipment. Other available resolutions included oversize aspects like SXGA+ and wide aspects like WXGA, WXGA+, WSXGA+, and WUXGA; monitors built to the 720p and 1080p standard were also not unusual among home media and video game players, due to the perfect screen compatibility with movie and video game releases. A new more-than-HD resolution of WQXGA was released in 30-inch LCD monitors in 2007.
In 2010, 27-inch LCD monitors with the resolution were released by multiple manufacturers, and in 2012, Apple introduced a display on the MacBook Pro. Panels for professional environments, such as medical use and air traffic control, support resolutions up to (or, more relevant for control rooms, pixels).
Common display resolutions
In recent years the 16:9 aspect ratio has become more common in notebook displays, and (HD) has become popular for most low-cost notebooks, while (FHD) and higher resolutions are available for more premium notebooks.
When a computer display resolution is set higher than the physical screen resolution (native resolution), some video drivers make the virtual screen scrollable over the physical screen thus realizing a two dimensional virtual desktop with its viewport. Most LCD manufacturers do make note of the panel's native resolution as working in a non-native resolution on LCDs will result in a poorer image, due to dropping of pixels to make the image fit (when using DVI) or insufficient sampling of the analog signal (when using VGA connector). Few CRT manufacturers will quote the true native resolution, because CRTs are analog in nature and can vary their display from as low as 320 × 200 (emulation of older computers or game consoles) to as high as the internal board will allow, or the image becomes too detailed for the vacuum tube to recreate (i.e., analog blur). Thus, CRTs provide a variability in resolution that fixed resolution LCDs cannot provide.
See also
Display aspect ratio
Display size
Pixel density of computer displays – PPI (for example, a 20-inch 1680 × 1050 screen has a PPI of 99.06)
Resolution independence
Ultrawide formats
Video scaler
Widescreen
References
Digital imaging
Display technology
Television technology
Television terminology
Video signal
Data compression | Display resolution | [
"Technology",
"Engineering"
] | 3,063 | [
"Information and communications technology",
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"Television technology",
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601,413 | https://en.wikipedia.org/wiki/Network%20security%20policy | A network security policy (NSP) is a generic document that outlines rules for computer network access, determines how policies are enforced and lays out some of the basic architecture of the company security/ network security environment. The document itself is usually several pages long and written by a committee.
A security policy is a complex document, meant to govern data access, web-browsing habits, use of passwords, encryption, email attachments and more. It specifies these rules for individuals or groups of individuals throughout the company. The policies could be expressed as a set of instructions that understood by special purpose network hardware dedicated for securing the network.
Security policy should keep the malicious users out, and also exert control over potential risky users within an organization.
Understanding what information and services are available and to which users, as well as what the potential is for damage and whether any protection is already in place to prevent misuse are important when writing a network security policy. In addition, the security policy should dictate a hierarchy of access permissions, granting users access only to what is necessary for the completion of their work. The National Institute of Standards and Technology provides an example security-policy guideline.
See also
Internet security
Security engineering
Computer security
Cybersecurity information technology list
Network security
Industrial espionage
Information security
Security policy
References
External links
Computer Security Resource Center at National Institute of Standards and Technology
Network Security Policy and Procedures document by the City of Madison, Wisconsin
Computer security procedures
Computer network security | Network security policy | [
"Engineering"
] | 296 | [
"Cybersecurity engineering",
"Computer network security",
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601,621 | https://en.wikipedia.org/wiki/Hubbert%20peak%20theory | The Hubbert peak theory says that for any given geographical area, from an individual oil-producing region to the planet as a whole, the rate of petroleum production tends to follow a bell-shaped curve. It is one of the primary theories on peak oil.
Choosing a particular curve determines a point of maximum production based on discovery rates, production rates, and cumulative production. Early in the curve (pre-peak), the production rate increases due to the discovery rate and the addition of infrastructure. Late in the curve (post-peak), production declines because of resource depletion.
The Hubbert peak theory is based on the observation that the amount of oil under the ground in any region is finite; therefore, the rate of discovery, which initially increases quickly, must reach a maximum and then decline. In the US, oil extraction followed the discovery curve after a time lag of 32 to 35 years. The theory is named after American geophysicist M. King Hubbert, who created a method of modeling the production curve given an assumed ultimate recovery volume.
Hubbert's peak
"Hubbert's peak" can refer to the peaking of production in a particular area, which has now been observed for many fields and regions.
Hubbert's peak was thought to have been achieved in the United States contiguous 48 states (that is, excluding Alaska and Hawaii) in the early 1970s. Oil production peaked at per day in 1970 and then declined over the subsequent 35 years in a pattern that closely followed the one predicted by Hubbert in the mid-1950s. However, beginning in the late 20th century, advances in extraction technology, particularly those that led to the extraction of tight oil and unconventional oil resulted in a large increase in U.S. oil production. Thus, establishing a pattern that deviated drastically from the model predicted by Hubbert for the contiguous 48-states as a whole. Production from Wells utilizing these advances extraction techniques, exhibit a rate of decline far greater than traditional means. In November 2017 the United States once again surpassed the 10 million barrel mark for the first time since 1970.
Peak oil as a proper noun, or "Hubbert's peak" applied more generally, refers to a predicted event: the peak of the entire planet's oil production. After peak oil, according to the Hubbert Peak Theory, the rate of oil production on Earth would enter a terminal decline. Based on his theory, in a paper he presented to the American Petroleum Institute in 1956, Hubbert correctly predicted that production of oil from conventional sources would peak in the continental United States around 1965–1970. Hubbert further predicted a worldwide peak at "about half a century" from publication and approximately 12 gigabarrels (GB) a year in magnitude. In a 1976 TV interview Hubbert added that the actions of OPEC might flatten the global production curve but this would only delay the peak for perhaps 10 years. The development of new technologies has provided access to large quantities of unconventional resources, and the boost in production has largely discounted Hubbert's prediction.
Hubbert's theory
Hubbert curve
In 1956, Hubbert proposed that fossil fuel production in a given region over time would follow a roughly bell-shaped curve without giving a precise formula; he later used the Hubbert curve, the derivative of the logistic curve, for estimating future production using past observed discoveries.
Hubbert assumed that after fossil fuel reserves (oil reserves, coal reserves, and natural gas reserves) are discovered, production at first increases approximately exponentially, as more extraction commences and more efficient facilities are installed. At some point, a peak output is reached, and production begins declining until it approximates an exponential decline.
The Hubbert curve satisfies these constraints. Furthermore, it is symmetrical, with the peak of production reached when half of the fossil fuel that will ultimately be produced has been produced. It also has a single peak.
Given past oil discovery and production data, a Hubbert curve that attempts to approximate past discovery data may be constructed and used to provide estimates for future production. In particular, the date of peak oil production or the total amount of oil ultimately produced can be estimated that way. Cavallo defines the Hubbert curve used to predict the U.S. peak as the derivative of:
where max is the total resource available (ultimate recovery of crude oil), the cumulative production, and and are constants. The year of maximum annual production (peak) is:
so now the cumulative production reaches the half of the total available resource:
The Hubbert equation assumes that oil production is symmetrical about the peak. Others have used similar but non-symmetrical equations which may provide better a fit to empirical production data.
Use of multiple curves
The sum of multiple Hubbert curves, a technique not developed by Hubbert himself, may be used in order to model more complicated real life scenarios. When new production methods, namely hydraulic fracturing, were pioneered on the previously unproductive oil-bearing Shale formations, the sudden, dramatic increase in production necessitated a distinct curve. Advances in technologies such as these are limited, but when a paradigm shifting idea impacts production and causes a need for a new curve to be added to the old curve, or the entire curve to be reworked. It should be noted, & it is well documented, that production from shale wells are unlike that of traditional well. A traditional oil well's rate of decline is shallow, & exhibits a slow, predictable rate of decline as the reservoir is drawn down (Drinking of Milkshake). Whereas production from shale wells, assuming successful fracturing, will see its peak production at the moment the well is brought in, with a drastic rate of decline shortly thereafter. However, one revolutionary aspect of these types of production methods are the ability to refracture the well. Production may be brought back up, to near peak levels with a reapplication of the fracturing technology to the subject formation. Once again releasing the hydrocarbons trapped tightly within the shale & allowing them to be drawn to the surface. This process allows the for an outward manipulation of the curve, simply by purposefully neglecting to rework the well until the operator's desired market conditions are present.
Reliability
Crude oil
Hubbert, in his 1956 paper, presented two scenarios for US crude oil production:
most likely estimate: a logistic curve with a logistic growth rate equal to 6%, an ultimate resource equal to 150 Giga-barrels (Gb) and a peak in 1965. The size of the ultimate resource was taken from a synthesis of estimates by well-known oil geologists and the US Geological Survey, which Hubbert judged to be the most likely case.
upper-bound estimate: a logistic curve with a logistic growth rate equal to 6% and ultimate resource equal to 200 Giga-barrels and a peak in 1970.
Hubbert's upper-bound estimate, which he regarded as optimistic, accurately predicted that US oil production would peak in 1970, although the actual peak was 17% higher than Hubbert's curve. Production declined, as Hubbert had predicted, and stayed within 10 percent of Hubbert's predicted value from 1974 through 1994; since then, actual production has been significantly greater than the Hubbert curve. The development of new technologies has provided access to large quantities of unconventional resources, and the boost of production has largely discounted Hubbert's prediction.
Hubbert's 1956 production curves depended on geological estimates of ultimate recoverable oil resources, but he was dissatisfied by the uncertainty this introduced, given the various estimates ranging from 110 billion to 590 billion barrels for the US. Starting in his 1962 publication, he made his calculations, including that of ultimate recovery, based only on mathematical analysis of production rates, proved reserves, and new discoveries, independent of any geological estimates of future discoveries. He concluded that the ultimate recoverable oil resource of the contiguous 48 states was 170 billion barrels, with a production peak in 1966 or 1967. He considered that because his model incorporated past technical advances, that any future advances would occur at the same rate, and were also incorporated. Hubbert continued to defend his calculation of 170 billion barrels in his publications of 1965 and 1967, although by 1967 he had moved the peak forward slightly, to 1968 or 1969.
A post-hoc analysis of peaked oil wells, fields, regions and nations found that Hubbert's model was the "most widely useful" (providing the best fit to the data), though many areas studied had a sharper "peak" than predicted.
A 2007 study of oil depletion by the UK Energy Research Centre pointed out that there is no theoretical and no robust practical reason to assume that oil production will follow a logistic curve. Neither is there any reason to assume that the peak will occur when half the ultimate recoverable resource has been produced; and in fact, empirical evidence appears to contradict this idea. An analysis of a 55 post-peak countries found that the average peak was at 25 percent of the ultimate recovery.
Natural gas
Hubbert also predicted that natural gas production would follow a logistic curve similar to that of oil. The graph shows actual gas production in blue compared to his predicted gas production for the United States in red, published in 1962.
Economics
Energy return on energy investment
The ratio of energy extracted to the energy expended in the process is often referred to as the Energy Return on Energy Investment (EROI or EROEI). Should the EROEI drops to one, or equivalently the Net energy gain falls to zero, the oil production is no longer a net energy source.
There is a difference between a barrel of oil, which is a measure of oil, and a barrel of oil equivalent (BOE), which is a measure of energy. Many sources of energy, such as fission, solar, wind, and coal, are not subject to the same near-term supply restrictions that oil is. Accordingly, even an oil source with an EROEI of 0.5 can be usefully exploited if the energy required to produce that oil comes from a cheap and plentiful energy source. Availability of cheap, but hard to transport, natural gas in some oil fields has led to using natural gas to fuel enhanced oil recovery. Similarly, natural gas in huge amounts is used to power most Athabasca tar sands plants. Cheap natural gas has also led to ethanol fuel produced with a net EROEI of less than 1, although figures in this area are controversial because methods to measure EROEI are in debate.
The assumption of inevitable declining volumes of oil and gas produced per unit of effort is contrary to recent experience in the US. In the United States, as of 2017, there has been an ongoing decade-long increase in the productivity of oil and gas drilling in all the major tight oil and gas plays. The US Energy Information Administration reports, for instance, that in the Bakken Shale production area of North Dakota, the volume of oil produced per day of drilling rig time in January 2017 was 4 times the oil volume per day of drilling five years previous, in January 2012, and nearly 10 times the oil volume per day of ten years previous, in January 2007. In the Marcellus gas region of the northeast, The volume of gas produced per day of drilling time in January 2017 was 3 times the gas volume per day of drilling five years previous, in January 2012, and 28 times the gas volume per day of drilling ten years previous, in January 2007.
Growth-based economic models
Insofar as economic growth is driven by oil consumption growth, post-peak societies must adapt. Hubbert believed:
Some economists describe the problem as uneconomic growth or a false economy. At the political right, Fred Ikle has warned about "conservatives addicted to the Utopia of Perpetual Growth". Brief oil interruptions in 1973 and 1979 markedly slowed—but did not stop—the growth of world GDP.
Between 1950 and 1984, as the Green Revolution transformed agriculture around the globe, world grain production increased by 250%. The energy for the Green Revolution was provided by fossil fuels in the form of fertilizers (natural gas), pesticides (oil), and hydrocarbon fueled irrigation.
David Pimentel, professor of ecology and agriculture at Cornell University, and Mario Giampietro, senior researcher at the National Research Institute on Food and Nutrition (INRAN), in their 2003 study Food, Land, Population and the U.S. Economy, placed the maximum U.S. population for a sustainable economy at 200 million (actual population approx. 290m in 2003, 329m in 2019). To achieve a sustainable economy world population will have to be reduced by two-thirds, says the study. Without population reduction, this study predicts an agricultural crisis beginning in 2020, becoming critical c. 2050. The peaking of global oil along with the decline in regional natural gas production may precipitate this agricultural crisis sooner than generally expected. Dale Allen Pfeiffer claims that coming decades could see spiraling food prices without relief and massive starvation on a global level such as never experienced before.
Hubbert peaks
Although Hubbert's peak theory receives the most attention concerning peak oil production, it has also been applied to other natural resources.
Natural gas
Doug Reynolds predicted in 2005 that the North American peak would occur in 2007. Bentley predicted a world "decline in conventional gas production from about 2020".
Coal
Although observers believe that peak coal is significantly further out than peak oil, Hubbert studied the specific example of anthracite in the US, a high-grade coal, whose production peaked in the 1920s. Hubbert found that anthracite matches a curve closely. Hubbert had recoverable coal reserves worldwide at 2.500 × 1012 metric tons and peaking around 2150 (depending on usage).
More recent estimates suggest an earlier peak. Coal: Resources and Future Production (PDF 630KB), published on April 5, 2007 by the Energy Watch Group (EWG), which reports to the German Parliament, found that global coal production could peak in as few as 15 years. Reporting on this, Richard Heinberg also notes that the date of peak annual energetic extraction from coal is likely to come earlier than the date of peak in quantity of coal (tons per year) extracted as the most energy-dense types of coal have been mined most extensively. A second study,
The Future of Coal by B. Kavalov and S. D. Peteves of the Institute for Energy (IFE), prepared for the European Commission Joint Research Centre, reaches similar conclusions and states that "coal might not be so abundant, widely available and reliable as an energy source in the future".
Work by David Rutledge of Caltech predicts that the total world coal production will amount to only about 450 gigatonnes. This implies that coal is running out faster than usually assumed.
Fissionable materials
In a paper in 1956, after a review of US fissionable reserves, Hubbert notes of nuclear power:
As of 2015, the identified resources of uranium are sufficient to provide more than 135 years of supply at the present rate of consumption. Technologies such as the thorium fuel cycle, reprocessing and fast breeders can, in theory, extend the life of uranium reserves from hundreds to thousands of years.
Caltech physics professor David Goodstein stated in 2004 that
Helium
Almost all helium on Earth is a result of radioactive decay of uranium and thorium. Helium is extracted by fractional distillation from natural gas, which contains up to 7% helium. The world's largest helium-rich natural gas fields are found in the United States, especially in the Hugoton and nearby gas fields in Kansas, Oklahoma, and Texas. The extracted helium is stored underground in the National Helium Reserve near Amarillo, Texas, the self-proclaimed "Helium Capital of the World". Helium production is expected to decline along with natural gas production in these areas.
Helium, which is the second-lightest chemical element, will rise to the upper layers of Earth's atmosphere, where it can forever break free from Earth's gravitational attraction. Approximately 1,600 tons of helium are lost per year as a result of atmospheric escape mechanisms.
Transition metals
Hubbert applied his theory to "rock containing an abnormally high concentration of a given metal" and reasoned that the peak production for metals such as copper, tin, lead, zinc and others would occur in the time frame of decades and iron in the time frame of two centuries like coal. The price of copper rose 500% between 2003 and 2007 and was attributed by some to peak copper. Copper prices later fell, along with many other commodities and stock prices, as demand shrank from fear of a global recession. Lithium availability is a concern for a fleet of Li-ion battery using cars but a paper published in 1996 estimated that world reserves are adequate for at least 50 years. A similar prediction for platinum use in fuel cells notes that the metal could be easily recycled.
Precious metals
In 2009, Aaron Regent president of the Canadian gold giant Barrick Gold said that global output has been falling by roughly one million ounces a year since the start of the decade. The total global mine supply has dropped by 10 percent as ore quality erodes, implying that the roaring bull market of the last eight years may have further to run. "There is a strong case to be made that we are already at 'peak gold'," he told The Daily Telegraph at the RBC's annual gold conference in London. "Production peaked around 2000 and it has been in decline ever since, and we forecast that decline to continue. It is increasingly difficult to find ore," he said.
Ore grades have fallen from around 12 grams per tonne in 1950 to nearer 3 grams in the US, Canada, and Australia. South Africa's output has halved since peaking in 1970. Output fell a further 14 percent in South Africa in 2008 as companies were forced to dig ever deeper – at greater cost – to replace depleted reserves.
World mined gold production has peaked four times since 1900: in 1912, 1940, 1971, and 2001, each peak being higher than previous peaks. The latest peak was in 2001 when production reached 2,600 metric tons, then declined for several years. Production started to increase again in 2009, spurred by high gold prices, and achieved record new highs each year in 2012, 2013, and 2014, when production reached 2,990 tonnes.
Phosphorus
Phosphorus supplies are essential to farming and depletion of reserves is estimated at somewhere from 60 to 130 years. According to a 2008 study, the total reserves of phosphorus are estimated to be approximately 3,200 MT, with peak production at 28 MT/year in 2034. Individual countries' supplies vary widely; without a recycling initiative America's supply is estimated around 30 years. Phosphorus supplies affect agricultural output which in turn limits alternative fuels such as biodiesel and ethanol. Its increasing price and scarcity (the global price of rock phosphate rose 8-fold in the 2 years to mid-2008) could change global agricultural patterns. Lands, perceived as marginal because of remoteness, but with very high phosphorus content, such as the Gran Chaco may get more agricultural development, while other farming areas, where nutrients are a constraint, may drop below the line of profitability.
Renewable resources
Wood
Unlike fossil resources, forests keep growing, thus the Hubbert peak theory does not apply. There had been wood shortages in the past, called Holznot in German-speaking regions, but no global peak wood yet, despite the early 2021 "Lumber Crisis". Besides, deforestation may cause other problems, like erosion and drought by ending forests' Biotic pump effect.
Water
Hubbert's original analysis did not apply to renewable resources. However, over-exploitation often results in a Hubbert peak nonetheless. A modified Hubbert curve applies to any resource that can be harvested faster than it can be replaced.
For example, a reserve such as the Ogallala Aquifer can be mined at a rate that far exceeds replenishment. This turns much of the world's underground water and lakes into finite resources with peak usage debates similar to oil. These debates usually center around agriculture and suburban water usage but generation of electricity from nuclear energy or coal and tar sands mining mentioned above is also water resource intensive. The term fossil water is sometimes used to describe aquifers whose water is not being recharged.
Fishing
At least one researcher has attempted to perform Hubbert linearization (Hubbert curve) on the whaling industry, as well as charting the transparently dependent price of caviar on sturgeon depletion. The Atlantic northwest cod fishery was a renewable resource, but the numbers of fish taken exceeded the fish's rate of recovery. The end of the cod fishery does match the exponential drop of the Hubbert bell curve. Another example is the cod of the North Sea.
Air/oxygen
Half the world's oxygen is produced by phytoplankton. The plankton was once thought to have dropped by 40% since the 1950s. However, the authors reanalyzed their data with better calibrations and found plankton abundance dropped globally by only a few percent over this time interval (Boyce et al. 2014)
Criticisms of peak oil
Economist Michael Lynch argues that the theory behind the Hubbert curve is simplistic and relies on an overly Malthusian point of view. Lynch claims that Campbell's predictions for world oil production are strongly biased towards underestimates, and that Campbell has repeatedly pushed back the date.
Leonardo Maugeri, vice president of the Italian energy company Eni, argues that nearly all of peak estimates do not take into account unconventional oil even though the availability of these resources is significant and the costs of extraction and processing, while still very high, are falling because of improved technology. He also notes that the recovery rate from existing world oil fields has increased from about 22% in 1980 to 35% today because of new technology and predicts this trend will continue. The ratio between proven oil reserves and current production has constantly improved, passing from 20 years in 1948 to 35 years in 1972 and reaching about 40 years in 2003. These improvements occurred even with low investment in new exploration and upgrading technology because of the low oil prices during the last 20 years. However, Maugeri feels that encouraging more exploration will require relatively high oil prices.
Edward Luttwak, an economist and historian, claims that unrest in countries such as Russia, Iran and Iraq has led to a massive underestimate of oil reserves. The Association for the Study of Peak Oil and Gas (ASPO) responds by claiming neither Russia nor Iran are troubled by unrest currently, but Iraq is.
Cambridge Energy Research Associates authored a report that is critical of Hubbert-influenced predictions:
CERA does not believe there will be an endless abundance of oil, but instead believes that global production will eventually follow an "undulating plateau" for one or more decades before declining slowly, and that production will reach 40 Mb/d by 2015.
Alfred J. Cavallo, while predicting a conventional oil supply shortage by no later than 2015, does not think Hubbert's peak is the correct theory to apply to world production.
Criticisms of peak element scenarios
Although M. King Hubbert himself made major distinctions between decline in petroleum production versus depletion (or relative lack of it) for elements such as fissionable uranium and thorium, some others have predicted peaks like peak uranium and peak phosphorus soon on the basis of published reserve figures compared to present and future production. According to some economists, though, the amount of proved reserves inventoried at a time may be considered "a poor indicator of the total future supply of a mineral resource."
As some illustrations, tin, copper, iron, lead, and zinc all had both production from 1950 to 2000 and reserves in 2000 much exceed world reserves in 1950, which would be impossible except for how "proved reserves are like an inventory of cars to an auto dealer" at a time, having little relationship to the actual total affordable to extract in the future. In the example of peak phosphorus, additional concentrations exist intermediate between 71,000 Mt of identified reserves (USGS) and the approximately 30,000,000,000 Mt of other phosphorus in Earth's crust, with the average rock being 0.1% phosphorus, so showing decline in human phosphorus production will occur soon would require far more than comparing the former figure to the 190 Mt/year of phosphorus extracted in mines (2011 figure).
See also
Abiogenic petroleum origin
Decline curve analysis
Fischer–Tropsch process
Food security
Hirsch report on peak oil
Kuznets curve
Limits to Growth
Low-carbon economy
Olduvai theory
Peak wheat
Reserves-to-production ratio
Sustainable agriculture
Transport energy futures: long-term oil supply trends and projections
Notes
References
"Feature on United States oil production." (November, 2002) ASPO Newsletter #23.
Greene, D.L. & J.L. Hopson. (2003). Running Out of and Into Oil: Analyzing Global Depletion and Transition Through 2050 ORNL/TM-2003/259, Oak Ridge National Laboratory, Oak Ridge, Tennessee, October
Economists Challenge Causal Link Between Oil Shocks And Recessions (August 30, 2004). Middle East Economic Survey VOL. XLVII No 35
Hubbert, M.K. (1982). Techniques of Prediction as Applied to Production of Oil and Gas, US Department of Commerce, NBS Special Publication 631, May 1982
Economic theories
Eponyms in economics
Peak oil
Petroleum politics
Energy and the environment | Hubbert peak theory | [
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"Petroleum",
"Petroleum politics"
] |
601,663 | https://en.wikipedia.org/wiki/List%20of%20monotremes%20and%20marsupials | The class Mammalia (mammals) is divided into two subclasses based on reproductive techniques: egg-laying mammals (yinotherians or monotremes - see also Australosphenida), and mammals which give live birth (therians). The latter subclass is divided into two infraclasses: pouched mammals (metatherians or marsupials), and placental mammals (eutherians, for which see List of placental mammals). Classification updated from Wilson and Reeder's "Mammal Species of the World: A Taxonomic and Geographic Reference" using the "Planet Mammifères" website.
Subclass Yinotheria (the monotremes)
Order Monotremata (monotremes, egg-laying mammals)
Family Ornithorhynchidae (platypus)
Genus Ornithorhynchus (platypus)
Platypus (Ornithorhynchus anatinus)
Family Tachyglossidae (echidnas)
Genus Tachyglossus (short-beaked echidna)
Short-beaked echidna (Tachyglossus aculeatus)
Genus Zaglossus (long-beaked echidnas)
Western long-beaked echidna (Zaglossus bruijnii)
Eastern long-beaked echidna (Zaglossus bartoni)
Sir David's long-beaked echidna (Zaglossus attenboroughi)
Subclass Theria
Infraclass Metatheria (marsupials)
Superorder Ameridelphia
Order Didelphimorphia (American opossums)
Family Didelphidae (opossums)
Subfamily Caluromyinae
Genus Caluromysiops
Black-shouldered opossum (Caluromysiops irrupta)
Genus Caluromys (woolly opossum)
Subgenus Caluromys
Bare-tailed woolly opossum (Caluromys philander)
Subgenus Mallodelphys
Derby's woolly opossum (Caluromys derbianus)
Brown-eared woolly opossum (Caluromys lanatus)
Subfamily Glironiinae
Genus Glironia
Bushy-tailed opossum (Glironia venusta)
Subfamily Hyladelphinae
Genus Hyladelphys
Kalinowski's mouse opossum (Hyladelphys kalinowskii)
Subfamily Didelphinae
Tribe Metachirini
Genus Metachirus
Brown four-eyed opossum (Metachirus myosuros)
Tribe Didelphini
Genus Chironectes
Yapok or water opossum (Chironectes minimus)
Genus Lutreolina
Massoia's lutrine opossum (Lutreolina massoia)
Big lutrine opossum or thick-tailed opossum (Lutreolina crassicaudata)
Genus Philander (gray and black four-eyed opossum)
Anderson's four-eyed opossum (Philander andersoni)
Deltaic four-eyed opossum (Philander deltae)
Southeastern four-eyed opossum (Philander frenatus)
McIlhenny's four-eyed opossum (Philander mcilhennyi)
Mondolfi's four-eyed opossum (Philander mondolfii)
Olrog's four-eyed opossum (Philander olrogi)
Gray four-eyed opossum (Philander opossum)
Genus Didelphis
White-eared opossum (Didelphis albiventris)
Big-eared opossum (Didelphis aurita)
Guianan white-eared opossum (Didelphis imperfecta)
Common opossum (Didelphis marsupialis)
Andean white-eared opossum (Didelphis pernigra)
Virginia opossum (Didelphis virginiana)
Tribe Thylamyini
Genus Chacodelphys
Chacoan pygmy opossum (Chacodelphys formosa)
Genus Cryptonanus
Agricola's gracile opossum (Cryptonanus agricolai)
Chacoan gracile opossum (Cryptonanus chacoensis)
Guahiba gracile opossum (Cryptonanus guahybae)
†Red-bellied gracile opossum (Cryptonanus ignitus)
Unduavi gracile opossum (Cryptonanus unduaviensis)
Genus Gracilinanus
Aceramarca gracile opossum (Gracilinanus aceramarcae)
Agile gracile opossum (Gracilinanus agilis)
Wood sprite gracile opossum (Gracilinanus dryas)
Emilia's gracile opossum (Gracilinanus emilae)
Northern gracile opossum (Gracilinanus marica)
Brazilian gracile opossum (Gracilinanus microtarsus)
Genus Lestodelphys
Patagonian opossum (Lestodelphys halli)
Genus Marmosops (slender opossum)
Bishop's slender opossum (Marmosops bishopi)
Narrow-headed slender opossum (Marmosops cracens)
Creighton's slender opossum (Marmosops creightoni)
Dorothy's slender opossum (Marmosops dorothea)
Dusky slender opossum (Marmosops fuscatus)
Handley's slender opossum (Marmosops handleyi)
Tschudi's slender opossum (Marmosops impavidus)
Gray slender opossum (Marmosops incanus)
Panama slender opossum (Marmosops invictus)
Junin slender opossum (Marmosops juninensis)
Neblina slender opossum (Marmosops neblina)
White-bellied slender opossum (Marmosops noctivagus)
Little spotted slender opossum (Marmosops ocellatus)
Delicate slender opossum (Marmosops parvidens)
Brazilian slender opossum (Marmosops paulensis)
Pinheiro's slender opossum (Marmosops pinheiroi)
Genus Thylamys (fat-tailed mouse opossum)
Cinderella fat-tailed mouse opossum (Thylamys cinderella)
Elegant fat-tailed mouse opossum (Thylamys elegans)
Karimi's fat-tailed mouse opossum (Thylamys karimii)
Paraguayan fat-tailed mouse opossum (Thylamys macrurus)
White-bellied fat-tailed mouse opossum (Thylamys pallidior)
Common fat-tailed mouse opossum (Thylamys pusillus)
Argentine fat-tailed mouse opossum (Thylamys sponsorius)
Tate's fat-tailed mouse opossum (Thylamys tatei)
Dwarf fat-tailed mouse opossum (Thylamys velutinus)
Buff-bellied fat-tailed mouse opossum (Thylamys venustus)
Tribe Marmosini
Genus Tlacuatzin
Gray mouse opossum (Tlacuatzin canescens)
Genus Marmosa (mouse opossum)
Subgenus Stegomarmosa
Heavy-browed mouse opossum (Marmosa andersoni)
Subgenus Marmosa
Isthmian mouse opossum (Marmosa isthmica)
Rufous mouse opossum (Marmosa lepida)
Mexican mouse opossum (Marmosa mexicana)
Linnaeus's mouse opossum (Marmosa murina)
Quechuan mouse opossum (Marmosa quichua)
Robinson's mouse opossum (Marmosa robinsoni)
Red mouse opossum (Marmosa rubra)
Tyler's mouse opossum (Marmosa tyleriana)
Guajira mouse opossum (Marmosa xerophila)
Subgenus Micoureus
Alston's mouse opossum (Marmosa alstoni)
White-bellied woolly mouse opossum (Marmosa constantiae)
Tate's woolly mouse opossum (Marmosa paraguayanus)
Little woolly mouse opossum (Marmosa phaeus)
Woolly mouse opossum (Marmosa demerarae)
Bare-tailed woolly mouse opossum (Marmosa regina)
Genus Monodelphis (short-tailed opossum)
Subgenus Minuania
Ronald's opossum (Monodelphis ronaldi)
Chestnut-striped opossum (Monodelphis rubida)
Reig's opossum (Monodelphis reigi)
Long-nosed short-tailed opossum (Monodelphis scalops)
Yellow-sided opossum (Monodelphis dimidiata)
Red three-striped opossum (Monodelphis umbristriata)
Subgenus Monodelphis
Sepia short-tailed opossum (Monodelphis adusta)
Amazonas short-tailed opossum (Monodelphis amazonica)
Northern three-striped opossum (Monodelphis americana)
Arlindo's opossum (Monodelphis arlindoi)
Northern red-sided opossum (Monodelphis brevicaudata)
Gray short-tailed opossum (Monodelphis domestica)
Emilia's short-tailed opossum (Monodelphis emiliae)
Gardner's short-tailed opossum (Monodelphis gardneri)
Amazonian red-sided opossum (Monodelphis glirina)
Handley's short-tailed opossum (Monodelphis handleyi)
Ihering's three-striped opossum (Monodelphis iheringi)
Pygmy short-tailed opossum (Monodelphis kunsi)
(Monodelphis macae)
Marajó short-tailed opossum (Monodelphis maraxina)
Obscure short-tailed opossum (Monodelphis obscura)
Osgood's short-tailed opossum (Monodelphis osgoodi)
Hooded red-sided opossum (Monodelphis palliolata)
(Monodelphis pinocchio)
Santa Rosa opossum (Monodelphis sanctaerosae)
Southern red-sided opossum (Monodelphis sorex)
Southern three-striped opossum (Monodelphis theresa)
One-striped opossum (Monodelphis unistriata)
Order Paucituberculata
Family Caenolestidae (shrew opossum)
Genus Lestoros
Incan caenolestid, (Lestoros inca)
Genus Rhyncholestes
Long-nosed caenolestid, (Rhyncholestes raphanurus)
Genus Caenolestes
Gray-bellied caenolestid, (Caenolestes caniventer)
Andean caenolestid, (Caenolestes condorensis)
Northern caenolestid, (Caenolestes convelatus)
Dusky caenolestid, (Caenolestes fuliginosus)
Superorder Australidelphia
Order Microbiotheria (monito del monte)
Family Microbiotheriidae
Genus Dromiciops
Monito del monte (Dromiciops gliroides)
Order Notoryctemorphia (marsupial moles)
Family Notoryctidae
Genus Notoryctes
Northern marsupial mole (Notoryctes caurinus)
Southern marsupial mole (Notoryctes typhlops)
Order Dasyuromorphia (marsupial carnivores)
Family †Thylacinidae
Genus †Thylacinus
†Thylacine (Thylacinus cynocephalus)
Family Myrmecobiidae
Genus Myrmecobius
Numbat (Myremecobius fasciatus)
Family Dasyuridae
Subfamily Dasyurinae
Tribe Dasyurini
Genus Dasycercus (mulgaras)
Crest-tailed mulgara, (Dasycercus cristicauda)
Genus Dasykaluta
Little red kaluta, (Dasykalua rosamondae)
Genus Dasyuroides
Kowari, (Dasyuroides byrnei)
Genus Dasyurus (quolls)
Subgenus Satanellus
Northern quoll, (Dasyurus hallucatus)
Subgenus Dasyurops
Tiger quoll, (Dasyurus maculatus)
Subgenus Dasyurinus
Western quoll, (Dasyurus geoffroii)
Subgenus Dasyurus
New Guinean quoll, (Dasyurus albopunctatus)
Bronze quoll, (Dasyurus spartacus)
Eastern quoll, (Dasyurus viverrinus)
Genus Myoictis
Woolley's three-striped dasyure (Myoictis leucera)
Three-striped dasyure, (Myoictis melas)
Wallace's dasyure, (Myoictis wallacii)
Tate's three-striped dasyure (Myoictis wavicus)
Genus Neophascogale
Speckled dasyure, (Neophascogale lorentzi)
Genus Parantechinus
Dibbler, (Parantechinus apicalis)
Genus Phascolosorex
Red-bellied marsupial shrew, (Phascolosorex doriae)
Narrow-striped marsupial shrew, (Phascolosorex dorsalis)
Genus Pseudantechinus
Sandstone dibbler, (Pseudantechinus bilarni)
Fat-tailed false antechinus, (Pseudantechinus macdonnellensis)
Alexandria false antechinus, (Pseudantechinus mimulus)
Ningbing false antechinus, (Pseudantechinus ningbing)
Rory Cooper's false antechinus, (Pseudantechinus roryi)
Woolley's false antechinus, (Pseudantechinus woolleyae)
Genus Sarcophilus
Tasmanian devil, (Sarcophilus harrisii)
Tribe Phascogalini
Genus Antechinus
Tropical antechinus, (Antechinus adustus)
Agile antechinus, (Antechinus agilis)
Silver-headed antechinus, (Antechinus argentus)
Black-tailed antechinus, (Antechinus arktos)
Fawn antechinus, (Antechinus bellus)
Yellow-footed antechinus, (Antechinus flaviceps)
Atherton antechinus, (Antechinus godmani)
Cinnamon antechinus, (Antechinus leo)
Swamp antechinus, (Antechinus minimus)
Buff-footed antechinus, (Antechinus mysticus)
Brown antechinus, (Antechinus stuartii)
Subtropical antechinus, (Antechinus subtropicus)
Dusky antechinus, (Antechinus swainsonii)
Tasman Peninsula Dusky antechinus, (Antechinus vandycki)
Genus Murexia
Subgenus Micromurexia
Habbema dasyure, (Murexia habbema)
Subgenus Murexechinus
Lesser antechinus, (Murexia wilhelmina)
Black-tailed dasyure, (Murexia melanurus)
Subgenus Murexia
Short-furred dasyure, (Murexia longicaudata)
Subgenus Paramurexia
Broad-striped dasyure, (Murexia rothschildi)
Subgenus Phascomurexia
Long-nosed dasyure, (Murexia naso)
Genus Phascogale
Red-tailed phascogale, (Phascogale calura)
Brush-tailed phascogale, (Phascogale tapoatafa)
Subfamily Sminthopsinae
Genus Sminthopsis
Subgenus Antechinomys
Kultarr, (Antechinomys laniger)
Subgenus Ningaui
Wongai ningaui, (Ningaui ridei)
Pilbara ningaui, (Ningaui timealeyi)
Southern ningaui, (Ningaui yvonneae)
Subgenus Sminthopsis
S. crassicaudata species-group
Fat-tailed dunnart, (Sminthopsis crassicaudata)
S. macroura species-group
Kakadu dunnart, (Sminthopsis bindi)
Carpentarian dunnart, (Sminthopsis butleri)
Julia Creek dunnart, (Sminthopsis douglasi)
Stripe-faced dunnart, (Sminthopsis macroura)
Red-cheeked dunnart, (Sminthopsis virginiae)
S. granulipes species-group
White-tailed dunnart, (Sminthopsis granulipes)
S. griseoventer species-group
Kangaroo Island dunnart, (Sminthopsis aitkeni)
Boullanger Island dunnart, (Sminthopsis boullangerensis)
Grey-bellied dunnart, (Sminthopsis griseoventer)
S. longicaudata species-group
Long-tailed dunnart, (Sminthopsis longicaudata)
S. murina species-group
Chestnut dunnart, (Sminthopsis archeri)
Little long-tailed dunnart, (Sminthopsis dolichura)
Sooty dunnart, (Sminthopsis fuliginosus)
Gilbert's dunnart, (Sminthopsis gilberti)
White-footed dunnart, (Sminthopsis leucopus)
Slender-tailed dunnart, (Sminthopsis murina)
S. psammophila species-group
Hairy-footed dunnart, (Sminthopsis hirtipes)
Ooldea dunnart, (Sminthopsis ooldea)
Sandhill dunnart, (Sminthopsis psammophila)
Lesser hairy-footed dunnart, (Sminthopsis youngsoni)
Genus Planigale
Paucident planigale, (Planigale gilesi)
Long-tailed planigale, (Planigale ingrami)
Common planigale, (Planigale maculata)
New Guinean planigale, (Planigale novaeguineae)
Narrow-nosed planigale, (Planigale tenuirostris)
Order Peramelemorphia (bandicoots and bilbies)
Family Thylacomyidae
Genus Macrotis (bilbies)
Greater bilby (Macrotis lagotis)
†Lesser bilby (Macrotis leucura)
Family Peramelidae
Genus Isoodon: short-nosed bandicoots
Golden bandicoot, (Isoodon auratus)
Northern brown bandicoot, (Isoodon macrourus)
Southern brown bandicoot, (Isoodon obesulus)
Genus Perameles: long-nosed bandicoots
Western barred bandicoot, (Perameles bougainville)
Eastern barred bandicoot, (Perameles gunnii)
Long-nosed bandicoot, (Perameles nasuta)
†Desert bandicoot, (Perameles eremiana)
Family †Chaeropodidae
Genus †Chaeropus (pig-footed bandicoots)
†Southern pig-footed bandicoot (Chaeropus ecaudatus)
†Northern pig-footed bandicoot (Chaeropus yirratji)
Family Peroryctidae (New Guinean bandicoots)
Subfamily Peroryctinae
Genus Peroryctes: New Guinean long-nosed bandicoots
Giant bandicoot, (Peroryctes broadbenti)
Raffray's bandicoot, (Peroryctes raffrayana)
Subfamily Echymiperinae
Genus Echymipera: New Guinean spiny bandicoots
Long-nosed spiny bandicoot, (Echymipera rufescens)
Clara's spiny bandicoot, (Echymipera clara)
Menzies' spiny bandicoot, (Echymipera echinista)
Common spiny bandicoot, (Echymipera kalubu)
David's spiny bandicoot, (Echymipera davidi)
Genus Microperoryctes : New Guinean mouse bandicoots
Papuan bandicoot, (Microperoryctes papuensis)
Subgenus Microperoryctes
Mouse bandicoot, (Microperoryctes murina)
Subgenus Ornoryctes
Eastern striped bandicoot, (Microperoryctes ornata)
Western striped bandicoot, (Microperoryctes longicauda)
Arfak pygmy bandicoot, (Microperoryctes aplini)
Genus Rhynchomeles
Seram bandicoot, (Rhynchomeles prattorum)
Order Diprotodontia (diprotodont marsupials)
Suborder Vombatiformes (wombats and koalas)
Family Phascolarctidae (koala)
Genus Phascolarctos
Koala (Phascolarctos cinereus)
Family Vombatidae (wombats)
Genus Lasiorhinus (hairy-nosed wombats)
Northern hairy-nosed wombat (Lasiorhinus krefftii)
Southern hairy-nosed wombat (Lasiorhinus latifrons)
Genus Vombatus (naked-nosed wombat)
Common wombat (Vombatus ursinus)
Suborder Phalangeriformes (possums and gliders)
Superfamily Phalangeroidea
Family Burramyidae: pygmy possums
Genus Burramys
Mountain pygmy possum (Burramys parvus)
Genus Cercartetus
Long-tailed pygmy possum (Cercartetus caudatus)
Southwestern pygmy possum (Cercartetus concinnus)
Tasmanian pygmy possum (Cercartetus lepidus)
Eastern pygmy possum (Cercartetus nanus)
Family Phalangeridae: brushtail possums and cuscuses
Subfamily Trichosurinae
Genus Trichosurus
Northern brushtail possum (Trichosurus arnhemensis)
Short-eared possum (Trichosurus caninus)
Mountain brushtail possum (Trichosurus cunninghami)
Coppery brushtail possum (Trichosurus johnstonii)
Common brushtail possum (Trichosurus vulpecula)
Genus Wyulda
Scaly-tailed possum (Wyulda squamicaudata)
Subfamily Ailuropinae
Genus Ailurops
Talaud bear cuscus (Ailurops melanotis)
Sulawesi bear cuscus (Ailurops ursinus)
Genus Strigocuscus
Sulawesi dwarf cuscus (Strigocuscus celebensis)
Banggai cuscus (Strigocuscus pelegensis)
Subfamily Phalangerinae
Genus Phalanger
Gebe cuscus (Phalanger alexandrae)
Mountain cuscus (Phalanger carmelitae)
Ground cuscus (Phalanger gymnotis)
Eastern common cuscus (Phalanger intercastellanus)
Woodlark cuscus (Phalanger lullulae)
Blue-eyed cuscus (Phalanger matabiru)
Telefomin cuscus (Phalanger matanim)
Southern common cuscus (Phalanger mimicus)
Northern common cuscus (Phalanger orientalis)
Ornate cuscus (Phalanger ornatus)
Rothschild's cuscus (Phalanger rothschildi)
Silky cuscus (Phalanger sericeus)
Stein's cuscus (Phalanger vestitus)
Genus Spilocuscus
Admiralty Island cuscus (Spilocuscus kraemeri)
Common spotted cuscus (Spilocuscus maculatus)
Waigeou cuscus (Spilocuscus papuensis)
Black-spotted cuscus (Spilocuscus rufoniger)
Blue-eyed spotted cuscus (Spilocuscus wilsoni)
Superfamily Petauroidea
Family Pseudocheiridae
Subfamily Hemibelideinae
Genus Hemibelideus
Lemur-like ringtail possum (Hemibelideus lemuroides)
Genus Petauroides
†New Guinea greater glider (Petauroides ayamaruensis)
Southern greater glider (Petauroides volans)
Northern greater glider (Petauroides minor)
Central greater glider (Petauroides armillatus)
Subfamily Pseudocheirinae
Genus Petropseudes
Rock-haunting ringtail possum (Petropseudes dahli)
Genus Pseudocheirus
Western ringtail possum (Pseudocheirus occidentalis)
Common ringtail possum (Pseudocheirus peregrinus)
Genus Pseudochirulus
Lowland ringtail possum (Pseudochirulus canescens)
Weyland ringtail possum (Pseudochirulus caroli)
Cinereus ringtail possum (Pseudochirulus cinereus)
Painted ringtail possum (Pseudochirulus forbesi)
Herbert River ringtail possum (Pseudochirulus herbertensis)
Masked ringtail possum (Pseudochirulus larvatus)
Pygmy ringtail possum (Pseudochirulus mayeri)
Vogelkop ringtail possum (Pseudochirulus schlegeli)
Subfamily Pseudochiropsinae
Genus Pseudochirops
D'Albertis' ringtail possum (Pseudochirops albertisii)
Green ringtail possum (Pseudochirops archeri)
Plush-coated ringtail possum (Pseudochirops corinnae)
Reclusive ringtail possum (Pseudochirops coronatus)
Coppery ringtail possum (Pseudochirops cupreus)
Family Petauridae
Subfamily Dactylopsilinae
Genus Dactylopsila
Subgenus Dactylonax
Long-fingered triok (Dactylopsila palpator)
Subgenus Dactylopsila
(Dactylopsila kambuayai)
Great-tailed triok (Dactylopsila megalura)
Tate's triok (Dactylopsila tatei)
Striped possum (Dactylopsila trivirgata)
Genus Gymnobelideus
Leadbeater's possum (Gymnobelideus leadbeateri)
Subfamily Petaurinae
Genus Petaurus
Northern glider (Petaurus abidi)
Yellow-bellied glider (Petaurus australis)
Biak glider (Petaurus biacensis)
Sugar glider (Petaurus breviceps)
Mahogany glider (Petaurus gracilis)
Squirrel glider (Petaurus norfolcensis)
Family Tarsipedidae
Genus Tarsipes
Honey possum (Tarsipes rostratus)
Family Acrobatidae
Genus Acrobates
Feathertail glider (Acrobates pygmaeus)
Genus Distoechurus
Feather-tailed possum (Distoechurus pennatus)
Suborder Macropodiformes (kangaroos, wallaroos, wallabies)
Family Macropodidae
Subfamily Sthenurinae
Genus Lagostrophus
Banded hare-wallaby (Lagostrophus fasciatus)
Subfamily Macropodinae
Genus Dendrolagus: tree-kangaroos
Grizzled tree-kangaroo (Dendrolagus inustus)
Lumholtz's tree-kangaroo (Dendrolagus lumholtzi)
Bennett's tree-kangaroo (Dendrolagus bennettianus)
Ursine tree-kangaroo (Dendrolagus ursinus)
Matschie's tree-kangaroo (Dendrolagus matschiei)
Doria's tree-kangaroo (Dendrolagus dorianus)
Goodfellow's tree-kangaroo (Dendrolagus goodfellowi)
Lowlands tree-kangaroo (Dendrolagus spadix)
Golden-mantled tree-kangaroo (Dendrolagus pulcherrimus)
Seri's tree-kangaroo (Dendrolagus stellarum)
Dingiso (Dendrolagus mbaiso)
Tenkile (Dendrolagus scottae)
Genus Dorcopsis
Brown dorcopsis (Dorcopsis muelleri)
White-striped dorcopsis (Dorcopsis hageni)
Black dorcopsis (Dorcopsis atrata)
Gray dorcopsis (Dorcopsis luctuosa)
Genus Dorcopsulus
Small dorcopsis (Dorcopsulus vanheurni)
Macleay's dorcopsis (Dorcopsulus macleayi)
Genus Lagorchestes
†Lake Mackay hare-wallaby (Lagorchestes asomatus)
Spectacled hare-wallaby (Lagorchestes conspicillatus)
Rufous hare-wallaby (Lagorchestes hirsutus)
†Eastern hare-wallaby (Lagorchestes leporides)
Genus Macropus: kangaroos and wallabies
Subgenus Notamacropus
Agile wallaby (Macropus agilis)
Black-striped wallaby (Macropus dorsalis)
Tammar wallaby (Macropus eugenii)
†Toolache wallaby (Macropus greyii)
Western brush wallaby (Macropus irma)
Parma wallaby: (Macropus parma) (rediscovered, thought extinct for 100 years)
Whiptail wallaby: (Macropus parryi)
Red-necked wallaby: (Macropus rufogriseus)
Subgenus Osphranter
Antilopine kangaroo (Macropus antilopinus)
Woodward's wallaroo (Macropus bernardus)
Eastern wallaroo (Macropus robustus)
Red kangaroo (Macropus rufus)
Subgenus Macropus
Western grey kangaroo (Macropus fuliginosus)
Eastern grey kangaroo (Macropus giganteus)
Genus Onychogalea
Bridled nail-tail wallaby (Onychogalea fraenata)
†Crescent nail-tail wallaby (Onychogalea lunata)
Northern nail-tail wallaby (Onychogalea unguifera)
Genus Petrogale
P. brachyotis species-group
Short-eared rock-wallaby (Petrogale brachyotis)
Monjon (Petrogale burbidgei)
Nabarlek (Petrogale concinna)
P. xanthopus species-group
Proserpine rock-wallaby (Petrogale persephone)
Rothschild's rock-wallaby (Petrogale rothschildi)
Yellow-footed rock-wallaby (Petrogale xanthopus)
P. lateralis/penicillata species-group
Allied rock-wallaby (Petrogale assimilis)
Cape York rock-wallaby (Petrogale coenensis)
Godman's rock-wallaby (Petrogale godmani)
Herbert's rock-wallaby (Petrogale herberti)
Unadorned rock-wallaby (Petrogale inornata)
Black-flanked rock-wallaby (Petrogale lateralis)
Mareeba rock-wallaby (Petrogale mareeba)
Brush-tailed rock-wallaby (Petrogale penicillata)
Purple-necked rock-wallaby (Petrogale purpureicollis)
Mount Claro rock-wallaby (Petrogale sharmani)
Genus Setonix
Quokka (Setonix brachyurus)
Genus Thylogale
Tasmanian pademelon (Thylogale billardierii)
Brown's pademelon (Thylogale browni)
Dusky pademelon (Thylogale brunii)
Calaby's pademelon (Thylogale calabyi)
Mountain pademelon (Thylogale lanatus)
Red-legged pademelon (Thylogale stigmatica)
Red-necked pademelon (Thylogale thetis)
Genus Wallabia
Swamp wallaby or black wallaby (Wallabia bicolor)
Family Potoroidae
Genus Aepyprymnus
Rufous rat-kangaroo (Aepyprymnus rufescens)
Genus Bettongia
Eastern bettong (Bettongia gaimardi)
Boodie (Bettongia lesueur)
Woylie (Bettongia penicillata)
Northern bettong (Bettongia tropica)
Genus Caloprymnus
†Desert rat-kangaroo (Caloprymnus campestris)
Genus Potorous
Gilbert's potoroo (Potorous gilbertii)
Long-footed potoroo (Potorous longipes)
†Broad-faced potoroo (Potorous platyops)
Long-nosed potoroo (Potorous tridactylus)
Family Hypsiprymnodontidae
Genus Hypsiprymnodon
Musky rat-kangaroo (Hypsiprymnodon moschatus)
See also
List of marsupials of Western Australia
Mammal classification
List of prehistoric mammals
List of recently extinct mammals
List of placental mammals
References
List
List
Monotremes and marsupials
Taxonomic lists | List of monotremes and marsupials | [
"Biology"
] | 7,047 | [
"Lists of biota",
"Taxonomy (biology)",
"Taxonomic lists"
] |
601,795 | https://en.wikipedia.org/wiki/Impression%20management | Impression management is a conscious or subconscious process in which people attempt to influence the perceptions of other people about a person, object or event by regulating and controlling information in social interaction. It was first conceptualized by Erving Goffman in 1956 in The Presentation of Self in Everyday Life, and then was expanded upon in 1967.
Impression management behaviors include accounts (providing "explanations for a negative event to escape disapproval"), excuses (denying "responsibility for negative outcomes"), and opinion conformity ("speak(ing) or behav(ing) in ways consistent with the target"), along with many others. By utilizing such behaviors, those who partake in impression management are able to control others' perception of them or events pertaining to them. Impression management is possible in nearly any situation, such as in sports (wearing flashy clothes or trying to impress fans with their skills), or on social media (only sharing positive posts). Impression management can be used with either benevolent or malicious intent.
Impression management is usually used synonymously with self-presentation, in which a person tries to influence the perception of their image. The notion of impression management was first applied to face-to-face communication, but then was expanded to apply to computer-mediated communication. The concept of impression management is applicable to academic fields of study such as psychology and sociology as well as practical fields such as corporate communication and media.
Background
The foundation and the defining principles of impression management were created by Erving Goffman in The Presentation of Self in Everyday Life. Impression management theory states that one tries to alter one's perception according to one's goals. In other words, the theory is about how individuals wish to present themselves, but in a way that satisfies their needs and goals. Goffman "proposed to focus on how people in daily work situations present themselves and, in so doing, what they are doing to others", and he was "particularly interested in how a person guides and controls how others form an impression of them and what a person may or may not do while performing before them".
Theory
Motives
A range of factors that govern impression management can be identified. It can be stated that impression management becomes necessary whenever there exists a kind of social situation, whether real or imaginary. Logically, the awareness of being a potential subject of monitoring is also crucial. Furthermore, the characteristics of a given social situation are important. Specifically, the surrounding cultural norms determine the appropriateness of particular nonverbal behaviours. The actions have to be appropriate to the targets, and within that culture, so that the kind of audience as well as the relation to the audience influences the way impression management is realized. A person's goals are another factor governing the ways and strategies of impression management. This refers to the content of an assertion, which also leads to distinct ways of presentation of aspects of the self. The degree of self-efficacy describes whether a person is convinced that it is possible to convey the intended impression.
A new study finds that, all other things being equal, people are more likely to pay attention to faces that have been associated with negative gossip than those with neutral or positive associations.
The study contributes to a body of work showing that far from being objective, human perceptions are shaped by unconscious brain processes that determine what they "choose" to see or ignore—even before they become aware of it. The findings also add to the idea that the brain evolved to be particularly sensitive to "bad guys" or cheaters—fellow humans who undermine social life by deception, theft or other non-cooperative behavior.
There are many methods behind self-presentation, including self disclosure (identifying what makes you "you" to another person), managing appearances (trying to fit in), ingratiation, aligning actions (making one's actions seem appealing or understandable), and alter-casting (imposing identities on other people). Maintaining a version of self-presentation that is generally considered to be attractive can help to increase one's social capital, and this method is commonly implemented by individuals at networking events. These self-presentation methods can also be used on the corporate level as impression management.
Self-presentation
Self-presentation is conveying information about oneself – or an image of oneself – to others. There are two types and motivations of self-presentation:
presentation meant to match one's own self-image, and
presentation meant to match audience expectations and preferences.
Self-presentation is expressive. Individuals construct an image of themselves to claim personal identity, and present themselves in a manner that is consistent with that image. If they feel like it is restricted, they often exhibit reactance or become defiant – try to assert their freedom against those who would seek to curtail self-presentation expressiveness. An example of this dynamic is someone who grew up with extremely strict or controlling parental figures. The child in this situation may feel that their identity and emotions have been suppressed, which may cause them to behave negatively towards others.
Boasting – Millon notes that in self-presentation individuals are challenged to balance boasting against discrediting themselves via excessive self-promotion or being caught and being proven wrong. Individuals often have limited ability to perceive how their efforts impact their acceptance and likeability by others.
Flattery – flattery or praise to increase social attractiveness
Intimidation – aggressively showing anger to get others to hear and obey one's demands.
Self-presentation can be either defensive or assertive strategies (also described as protective versus acquisitive). Whereas defensive strategies include behaviours like avoidance of threatening situations or means of self-handicapping, assertive strategies refer to more active behaviour like the verbal idealisation of the self, the use of status symbols or similar practices.
These strategies play important roles in one's maintenance of self-esteem. One's self-esteem is affected by their evaluation of their own performance and their perception of how others react to their performance. As a result, people actively portray impressions that will elicit self-esteem enhancing reactions from others.
In 2019, as filtered photos are perceived as deceptive by users, PlentyOfFish along with other dating sites have started to ban filtered images.
Social interaction
Goffman argued in his 1967 book, Interaction ritual, that people participate in social interactions by performing a "line", or "pattern of verbal and nonverbal acts", which is created and maintained by both the performer and the audience. By enacting a line effectively, the person gains positive social value, which is also called "face". The success of a social interaction will depend on whether the performer has the ability to maintain face. As a result, a person is required to display a kind of character by becoming "someone who can be relied upon to maintain himself as an interactant, poised for communication, and to act so that others do not endanger themselves by presenting themselves as interactants to him". Goffman analyses how a human being in "ordinary work situations presents himself and his activity to others, the ways in which he guides and controls the impression they form of him, and the kinds of things he may and may not do while sustaining his performance before them".
When Goffman turned to focus on people physically presented in a social interaction, the "social dimension of impression management certainly extends beyond the specific place and time of engagement in the organization". Impression management is "a social activity that has individual and community implications". We call it "pride" when a person displays a good showing from duty to himself, while we call it "honor" when he "does so because of duty to wider social units, and receives support from these duties in doing so".
Another approach to moral standards that Goffman pursues is the notion of "rules of conduct", which "can be partially understood as obligations or moral constraints". These rules may be substantive (involving laws, morality, and ethics) or ceremonial (involving etiquette). Rules of conduct play an important role when a relationship "is asymmetrical and the expectations of one person toward another are hierarchical."
Dramaturgical analogy
Goffman presented impression management dramaturgically, explaining the motivations behind complex human performances within a social setting based on a play metaphor. Goffman's work incorporates aspects of a symbolic interactionist perspective, emphasizing a qualitative analysis of the interactive nature of the communication process. Impression management requires the physical presence of others. Performers who seek certain ends in their interest, must "work to adapt their behavior in such a way as to give off the correct impression to a particular audience" and "implicitly ask that the audience take their performance seriously". Goffman proposed that while among other people individual would always strive to control the impression that others form of him or her so that to achieve individual or social goals.
The actor, shaped by the environment and target audience, sees interaction as a performance. The objective of the performance is to provide the audience with an impression consistent with the desired goals of the actor. Thus, impression management is also highly dependent on the situation. In addition to these goals, individuals differ in responses from the interactive environment, some may be non-responsive to an audience's reactions while others actively respond to audience reactions in order to elicit positive results. These differences in response towards the environment and target audience are called self-monitoring. Another factor in impression management is self-verification, the act of conforming the audience to the person's self-concept.
The audience can be real or imaginary. IM style norms, part of the mental programming received through socialization, are so fundamental that we usually do not notice our expectations of them. While an actor (speaker) tries to project a desired image, an audience (listener) might attribute a resonant or discordant image. An example is provided by situations in which embarrassment occurs and threatens the image of a participant.
Goffman proposes that performers "can use dramaturgical discipline as a defense to ensure that the 'show' goes on without interruption." Goffman contends that dramaturgical discipline includes:
coping with dramaturgical contingencies;
demonstrating intellectual and emotional involvement;
remembering one's part and not committing unmeant gestures or faux pas;
not giving away secrets involuntarily;
covering up inappropriate behavior on the part of teammates on the spur of the moment;
offering plausible reasons or deep apologies for disruptive events;
maintaining self-control (for example, speaking briefly and modestly);
suppressing emotions to private problems; and
suppressing spontaneous feelings.
Manipulation and ethics
In business, "managing impressions" normally "involves someone trying to control the image that a significant stakeholder has of them". The ethics of impression management has been hotly debated on whether we should see it as an effective self-revelation or as cynical manipulation. Some people insist that impression management can reveal a truer version of the self by adopting the strategy of being transparent. Because transparency "can be provided so easily and because it produces information of value to the audience, it changes the nature of impression management from being cynically manipulative to being a kind of useful adaptation".
Virtue signalling is used within groups to criticize their own members for valuing outward appearance over substantive action (having a real or permanent, rather than apparent or temporary, existence).
Psychological manipulation is a type of social influence that aims to change the behavior or perception of others through abusive, deceptive, or underhanded tactics. By advancing the interests of the manipulator, often at another's expense, such methods could be considered exploitative, abusive, devious, and deceptive. The process of manipulation involves bringing an unknowing victim under the domination of the manipulator, often using deception, and using the victim to serve their own purposes.
Machiavellianism is a term that some social and personality psychologists use to describe a person's tendency to be unemotional, and therefore able to detach him or herself from conventional morality and hence to deceive and manipulate others. (See also Machiavellianism in the workplace.)
Lying constitutes a force that is destructive and can manipulate an environment allowing them to be narcissistic human beings. A person's mind can be manipulated into believing those antics are true as though it relates to being solely deceptive and unethical. Theories show manipulation can cause a huge effect on the dynamic of one's relationship. The emotions of a person can stem from a trait that is mistrustful, triggering one's attitude and character to misbehave disapprovingly. Relationships with a positive force can provide a greater exchange whereas with relationships having poor moral values, the chances of the connection will be based on detachment and disengagement. Dark personalities and manipulation are within the same entity. It will intervene between a person's attainable goal if their perspective is only focused on self-centeredness. The personality entices a range of erratic behaviors that will corrupt the mind into practicing violent acts resulting in a rage of anger and physical harm.
Public relations Ethics. Professionals both serve the public's interest and private interests of businesses, associations, non-profit organizations, and governments. This dual obligation gave rise to heated debates among scholars of the discipline and practitioners over its fundamental values. This conflict represents the main ethical predicament of public relations.[40] In 2000, the Public Relations Society of America (PRSA) responded to the controversy by acknowledging in its new code of ethics "advocacy" – for the first time – as a core value of the discipline.[40]
The field of public relations is generally highly un-regulated, but many professionals voluntarily adhere to the code of conduct of one or more professional bodies to avoid exposure for ethical violations.[41] The Chartered Institute of Public Relations, the Public Relations Society of America, and The Institute of Public Relations are a few organizations that publish an ethical code. Still, Edelman's 2003 semi-annual trust survey found that only 20 percent of survey respondents from the public believed paid communicators within a company were credible.[42] Individuals in public relations are growing increasingly concerned with their company's marketing practices, questioning whether they agree with the company's social responsibility. They seek more influence over marketing and more of a counseling and policy-making role. On the other hand, individuals in marketing are increasingly interested in incorporating publicity as a tool within the realm marketing.[43]
According to Scott Cutlip, the social justification for public relations is the right for an organization to have a fair hearing of their point of view in the public forum, but to obtain such a hearing for their ideas requires a skilled advocate.[44]
Marketing and communications strategist, Ira Gostin, believes there is a code of conduct when conducting business and using public relations. Public relations specialists have the ability to influence society. Fact-checking and presenting accurate information is necessary to maintain credibility with employers and clients.[45]
Public Relations
Code of Ethics
The Public Relation Student Society of America has established a set of fundamental guidelines that people within the public relations professions should practice and use in their business atmosphere. These values are:
Advocacy: Serving the public interest by acting as responsible advocates for the clientele. This can occur by displaying the marketplace of ideas, facts and viewpoints to aid informed public debate.
Honesty: Standing by the truth and accuracy of all facts in the case and advancing those statements to the public.
Expertise: To become and stay informed of the specialized knowledge needed in the field of Public Relations. Taking that knowledge and improving the field through development, research and education. Meanwhile, professionals also build their understanding, credibility, and relationships to understand various audiences and industries.
Independence: Provide unbiased work to those that are represented while being accountable for all actions.
Loyalty: Stay devoted to the client while remembering that there is a duty to still serve the public interest.
Fairness: Honorably conduct business with any and all clients, employers, competitors, peers, vendors, media and general public. Respecting all opinions and right of free expression.[46]
International Public Relations Code of Ethics
Other than the ethics put in place in the United States of America there are also International ethics set to ensure proper and, legal worldwide communication. Regarding these ethics, there are broad codes used specifically for international forms of public relations, and then there are more specific forms from different countries. For example, some countries have certain associations to create ethics and standards to communication across their country.
The International Association of Business Communication (founded in 1971),[47] or also known as IABC, has its own set of ethics in order to enforce a set of guidelines that ensure communication internationality is legal, ethical, and is in good taste. Some principles that members of the board of IABC follow include.
Having proper and legal communication
Being understanding and open to other people's cultures, values, and beliefs
Create communication that is accurate, trusting, to ensure mutual respect and understanding
The IABC members use the following list of ethics in order to work to improve values of communication throughout the world:[47]
Being credible and honest
Keeping up with information to ensure accuracy of communication
Understanding free speech and respecting this right
Having sensitivity towards other people's thoughts, beliefs, and way of life
Not taking part in unethical behaviors
Obeying policies and laws
Giving proper credit to resources used for communication
Ensuring private information is protected (not used for personal gain) and if publicized, guarantee proper legal measures will be put in place.
Publishers of said communication do not accept gifts, benefits, payments etc.; for work, or their services
Creating results and spreading results that are attainable and they can deliver.
Being fully truthful to other people, and themselves.
Media is a major resource in the public relations career especially in news networks. That is why as a public relations specialist, having proper information is very important, and crucial to the society as a whole.
Spin
Main article: Spin (public relations)
Spin has been interpreted historically to mean overt deceit that is meant to manipulate the public, but since the 1950s has shifted to describing a "polishing of the truth."[48] Today, spin refers to providing a certain interpretation of information meant to sway public opinion.[49] Companies may use spin to create the appearance of the company or other events are going in a slightly different direction than they actually are.[48] Within the field of public relations, spin is seen as a derogatory term, interpreted by professionals as meaning blatant deceit and manipulation.[50][51] Skilled practitioners of spin are sometimes called "spin doctors."
In Stuart Ewen's PR! A Social History of Spin, he argues that public relations can be a real menace to democracy as it renders the public discourse powerless. Corporations are able to hire public relations professionals and transmit their messages through the media channels and exercise a huge amount of influence upon the individual who is defenseless against such a powerful force. He claims that public relations is a weapon for capitalist deception and the best way to resist is to become media literate and use critical thinking when interpreting the various mediated messages.[52]
According to Jim Hoggan, "public relations is not by definition 'spin'. Public relations is the art of building good relationships. You do that most effectively by earning trust and goodwill among those who are important to you and your business... Spin is to public relations what manipulation is to interpersonal communications. It's a diversion whose primary effect is ultimately to undermine the central goal of building trust and nurturing a good relationship."[53]
The techniques of spin include selectively presenting facts and quotes that support ideal positions (cherry picking), the so-called "non-denial denial", phrasing that in a way presumes unproven truths, euphemisms for drawing attention away from items considered distasteful, and ambiguity in public statements. Another spin technique involves careful choice of timing in the release of certain news so it can take advantage of prominent events in the news.
Negative
See also: Negative campaigning
Negative public relations, also called dark public relations (DPR), 'black hat PR' and in some earlier writing "Black PR", is a process of destroying the target's reputation and/or corporate identity. The objective in DPR is to discredit someone else, who may pose a threat to the client's business or be a political rival. DPR may rely on IT security, industrial espionage, social engineering and competitive intelligence. Common techniques include using dirty secrets from the target, producing misleading facts to fool a competitor.[54][55][56][57] In politics, a decision to use negative PR is also known as negative campaigning.
Application
Face-to-face communication
Self, social identity and social interaction
The social psychologist, Edward E. Jones, brought the study of impression management to the field of psychology during the 1960s and extended it to include people's attempts to control others' impression of their personal characteristics. His work sparked an increased attention towards impression management as a fundamental interpersonal process.
The concept of self is important to the theory of impression management as the images people have of themselves shape and are shaped by social interactions. Our self-concept develops from social experience early in life. Schlenker (1980) further suggests that children anticipate the effect that their behaviours will have on others and how others will evaluate them. They control the impressions they might form on others, and in doing so they control the outcomes they obtain from social interactions.
Social identity refers to how people are defined and regarded in social interactions. Individuals use impression management strategies to influence the social identity they project to others. The identity that people establish influences their behaviour in front of others, others' treatment of them and the outcomes they receive. Therefore, in their attempts to influence the impressions others form of themselves, a person plays an important role in affecting his social outcomes.
Social interaction is the process by which we act and react to those around us. In a nutshell, social interaction includes those acts people perform toward each other and the responses they give in return. The most basic function of self-presentation is to define the nature of a social situation (Goffman, 1959). Most social interactions are very role governed. Each person has a role to play, and the interaction proceeds smoothly when these roles are enacted effectively. People also strive to create impressions of themselves in the minds of others in order to gain material and social rewards (or avoid material and social punishments).
Cross-cultural communication
Understanding how one's impression management behavior might be interpreted by others can also serve as the basis for smoother interactions and as a means for solving some of the most insidious communication problems among individuals of different racial/ethnic and gender backgrounds (Sanaria, 2016).
"People are sensitive to how they are seen by others and use many forms of impression management to compel others to react to them in the ways they wish" (Giddens, 2005, p. 142). An example of this concept is easily illustrated through cultural differences. Different cultures have diverse thoughts and opinions on what is considered beautiful or attractive. For example, Americans tend to find tan skin attractive, but in Indonesian culture, pale skin is more desirable. It is also argued that Women in India use different impression management strategies as compared to women in western cultures (Sanaria, 2016).
Another illustration of how people attempt to control how others perceive them is portrayed through the clothing they wear. A person who is in a leadership position strives to be respected and in order to control and maintain the impression. This illustration can also be adapted for a cultural scenario. The clothing people choose to wear says a great deal about the person and the culture they represent. For example, most Americans are not overly concerned with conservative clothing. Most Americans are content with tee shirts, shorts, and showing skin. The exact opposite is true on the other side of the world. "Indonesians are both modest and conservative in their attire" (Cole, 1997, p. 77).
One way people shape their identity is through sharing photos on social media platforms. The ability to modify photos by certain technologies, such as Photoshop, helps achieve their idealized images.
Companies use cross-cultural training (CCT) to facilitate effective cross-cultural interaction. CCT can be defined as any procedure used to increase an individual's ability to cope with and work in a foreign environment. Training employees in culturally consistent and specific impression management (IM) techniques provide the avenue for the employee to consciously switch from an automatic, home culture IM mode to an IM mode that is culturally appropriate and acceptable. Second, training in IM reduces the uncertainty of interaction with FNs and increases employee's ability to cope by reducing unexpected events.
Team-working in hospital wards
Impression management theory can also be used in health communication. It can be used to explore how professionals 'present' themselves when interacting on hospital wards and also how they employ front stage and backstage settings in their collaborative work.
In the hospital wards, Goffman's front stage and backstage performances are divided into 'planned' and 'ad hoc' rather than 'official' and 'unofficial' interactions.
Planned front stage is the structured collaborative activities such as ward rounds and care conferences which took place in the presence of patients and/or carers.
Ad hoc front stage is the unstructured or unplanned interprofessional interactions that took place in front of patients/carers or directly involved patients/carers.
Planned backstage is the structured multidisciplinary team meeting (MDT) in which professionals gathered in a private area of the ward, in the absence of patients, to discuss management plans for patients under their care.
Ad hoc backstage is the use of corridors and other ward spaces for quick conversations between professionals in the absence of patients/carers.
Offstage is the social activities between and among professional groups/individuals outside of the hospital context.
Results show that interprofessional interactions in this setting are often based less on planned front stage activities than on ad hoc backstage activities. While the former may, at times, help create and maintain an appearance of collaborative interprofessional 'teamwork', conveying a sense of professional togetherness in front of patients and their families, they often serve little functional practice. These findings have implications for designing ways to improve interprofessional practice on acute hospital wards where there is no clearly defined interprofessional team, but rather a loose configuration of professionals working together in a collaborative manner around a particular patient. In such settings, interventions that aim to improve both ad hoc as well as planned forms of communication may be more successful than those intended to only improve planned communication.
Computer-mediated communication
The hyperpersonal model of computer-mediated communication (CMC) posits that users exploit the technological aspects of CMC in order to enhance the messages they construct to manage impressions and facilitate desired relationships. The most interesting aspect of the advent of CMC is how it reveals basic elements of interpersonal communication, bringing into focus fundamental processes that occur as people meet and develop relationships relying on typed messages as the primary mechanism of expression. "Physical features such as one's appearance and voice provide much of the information on which people base first impressions face-to-face, but such features are often unavailable in CMC. Various perspectives on CMC have suggested that the lack of nonverbal cues diminishes CMC's ability to foster impression formation and management, or argued impressions develop nevertheless, relying on language and content cues. One approach that describes the way that CMC's technical capacities work in concert with users' impression development intentions is the hyperpersonal model of CMC (Walther, 1996). As receivers, CMC users idealize partners based on the circumstances or message elements that suggest minimal similarity or desirability. As senders, CMC users selectively self-present, revealing attitudes and aspects of the self in a controlled and socially desirable fashion. The CMC channel facilitates editing, discretion, and convenience, and the ability to tune out environmental distractions and re-allocate cognitive resources in order to further enhance one's message composition. Finally, CMC may create dynamic feedback loops wherein the exaggerated expectancies are confirmed and reciprocated through mutual interaction via the bias-prone communication processes identified above."
According to O'Sullivan's (2000) impression management model of communication channels, individuals will prefer to use mediated channels rather than face-to-face conversation in face-threatening situations. Within his model, this trend is due to the channel features that allow for control over exchanged social information. The present paper extends O'Sullivan's model by explicating information control as a media affordance, arising from channel features and social skills, that enables an individual to regulate and restrict the flow of social information in an interaction, and present a scale to measure it. One dimension of the information control scale, expressive information control, positively predicted channel preference for recalled face-threatening situations. This effect remained after controlling for social anxiousness and power relations in relationships. O'Sullivan's model argues that some communication channels may help individuals manage this struggle and therefore be more preferred as those situations arise. It was based on an assumption that channels with features that allow fewer social cues, such as reduced nonverbal information or slower exchange of messages, invariably afford an individual with an ability to better manage the flow of a complex, ambiguous, or potentially difficult conversations. Individuals manage what information about them is known, or isn't known, to control other's impression of them. Anyone who has given the bathroom a quick cleaning when they anticipate the arrival of their mother-in-law (or date) has managed their impression. For an example from information and communication technology use, inviting someone to view a person's Webpage before a face-to-face meeting may predispose them to view the person a certain way when they actually meet.
Corporate brand
The impression management perspective offers potential insight into how corporate stories could build the corporate brand, by influencing the impressions that stakeholders form of the organization. The link between themes and elements of corporate stories and IM strategies/behaviours indicates that these elements will influence audiences' perceptions of the corporate brand.
Corporate storytelling
Corporate storytelling is suggested to help demonstrate the importance of the corporate brand to internal and external stakeholders, and create a position for the company against competitors, as well as help a firm to bond with its employees (Roper and Fill, 2012). The corporate reputation is defined as a stakeholder's perception of the organization (Brown et al., 2006), and Dowling (2006) suggests that if the story causes stakeholders to perceive the organization as more authentic, distinctive, expert, sincere, powerful, and likeable, then it is likely that this will enhance the overall corporate reputation.
Impression management theory is a relevant perspective to explore the use of corporate stories in building the corporate brand. The corporate branding literature notes that interactions with brand communications enable stakeholders to form an impression of the organization (Abratt and Keyn, 2012), and this indicates that IM theory could also therefore bring insight into the use of corporate stories as a form of communication to build the corporate brand. Exploring the IM strategies/behaviors evident in corporate stories can indicate the potential for corporate stories to influence the impressions that audiences form of the corporate brand.
Corporate document
Firms use more subtle forms of influencing outsiders' impressions of firm performance and prospects, namely by manipulating the content and presentation of information in corporate documents with the purpose of "distort[ing] readers" perceptions of corporate achievements" [Godfrey et al., 2003, p. 96]. In the accounting literature this is referred to as impression management. The opportunity for impression management in corporate reports is increasing. Narrative disclosures have become longer and more sophisticated over the last few years. This growing importance of descriptive sections in corporate documents provides firms with the opportunity to overcome information asymmetries by presenting more detailed information and explanation, thereby increasing their decision-usefulness. However, they also offer an opportunity for presenting financial performance and prospects in the best possible light, thus having the opposite effect. In addition to the increased opportunity for opportunistic discretionary disclosure choices, impression management is also facilitated in that corporate narratives are largely unregulated.
Media
The medium of communication influences the actions taken in impression management. Self-efficacy can differ according to the fact whether the trial to convince somebody is made through face-to-face-interaction or by means of an e-mail. Communication via devices like telephone, e-mail or chat is governed by technical restrictions, so that the way people express personal features etc. can be changed. This often shows how far people will go.
The affordances of a certain medium also influence the way a user self-presents. Communication via a professional medium such as e-mail would result in professional self-presentation. The individual would use greetings, correct spelling, grammar and capitalization as well as scholastic language. Personal communication mediums such as text-messaging would result in a casual self-presentation where the user shortens words, includes emojis and selfies and uses less academic language.
Another example of impression management theory in play is present in today's world of social media. Users are able to create a profile and share whatever they like with their friends, family, or the world. Users can choose to omit negative life events and highlight positive events if they so please.
Profiles on social networking sites
Social media usage among American adults grew from 5% in 2005 to 69% in 2018. Facebook is the most popular social media platform, followed by Instagram, LinkedIn, and Twitter.
Social networking users will employ protective self-presentations for image management. Users will use subtractive and repudiate strategies to maintain a desired image. Subtractive strategy is used to untag an undesirable photo on Social Networking Sites. In addition to un-tagging their name, some users will request the photo to be removed entirely. Repudiate strategy is used when a friend posts an undesirable comment about the user. In response to an undesired post, users may add another wall post as an innocence defense. Michael Stefanone states that "self-esteem maintenance is an important motivation for strategic self-presentation online." Outside evaluations of their physical appearance, competence, and approval from others determines how social media users respond to pictures and wall posts. Unsuccessful self-presentation online can lead to rejection and criticism from social groups. Social media users are motivated to actively participate in SNS from a desire to manage their online image.
Online social media presence often varies with respect to users' age, gender, and body weight. While men and women tend to use social media in comparable degrees, both uses and capabilities vary depending on individual preferences as well perceptions of power or dominance. In terms of performance, men tend to display characteristics associated with masculinity as well as more commanding language styles. In much the same way, women tend to present feminine self-depictions and engage in more supportive language.
With respect to usage across age variances, many children develop digital and social media literacy skills around 7 or 8 and begin to form online social relationships via virtual environments designed for their age group. The years between thirteen and fifteen demonstrate high social media usage that begins to become more balanced with offline interactions as teens learn to navigate both their online and in-person identities which may often diverge from one another.
Social media platforms often provide a great degree of social capital during the college years and later. College students are motivated to use Facebook for impression management, self-expression, entertainment, communication and relationship maintenance. College students sometimes rely on Facebook to build a favorable online identity, which contributes to greater satisfaction with campus life. In building an online persona, college students sometimes engage in identity manipulation, including altering personality and appearance, to increase their self-esteem and appear more attractive to peers. Since risky behavior is frequently deemed attractive by peers, college students often use their social media profiles to gain approval by highlighting instances of risky behavior, like alcohol use and unhealthy eating. Users present risky behavior as signs of achievement, fun, and sociability, participating in a form of impression management aimed at building recognition and acceptance among peers. During middle adulthood, users tend to display greater levels of confidence and mastery in their social media connections while older adults tend to use social media for educational and supportive purposes. These myriad factors influence how users will form and communicate their online personas. In addition to that, TikTok has made an influence on college students and adults to create their own self-image on a social media platform. The positivity of this is that college students and adults are using this to create their own brand for business purposes and for entertainment purposes. This gives them a chance to seek the desires of stardom and build an audience for revenue. Media fatigue is a negative effect that is caused by the conveyance of social media presence. Social anxiety stems from low-self esteem which causes a strain of stress in one's self-identity that is perceived in the media limelight for targeted audiences.
According to Marwick, social profiles create implications such as "context collapse" for presenting oneself to the audience. The concept of 'context collapse' suggests that social technologies make it difficult to vary self-presentation based on environment or audience. "Large sites such as Facebook and Twitter group friends, family members, coworkers, and acquaintances together under the umbrella term 'friends'." In a way, this context collapse is aided by a notion of performativity as characterized by Judith Butler.
Political impression management
Impression management is also influential in the political spectrum. "Political impression management" was coined in 1972 by sociologist Peter M. Hall, who defined the term as the art of marking a candidate look electable and capable (Hall, 1972). This is due in part to the importance of "presidential" candidates—appearance, image, and narrative are a key part of a campaign and thus impression management has always been a huge part of winning an election (Katz 2016). Social media has evolved to be part of the political process, thus political impression management is becoming more challenging as the online image of the candidate often now lies in the hands of the voters themselves.
The evolution of social media has increased the way in which political campaigns are targeting voters and how influential impression management is when discussing political issues and campaigns. Political campaigns continue to use social media as a way to promote their campaigns and share information about who they are to make sure to lead the conversation about their political platform. Research has shown that political campaigns must create clear profiles for each candidate in order to convey the right message to potential voters.
In the workplace
In professional settings, impression management is usually primarily focused on appearing competent, but also involves constructing and displaying an image of oneself that others find socially desirable and believably authentic. People manage impressions by their choice of dress, dressing either more or less formally, and this impacts perceptions their coworkers and supervisors form. The process includes a give and take; the person managing their impression receives feedback as the people around them interact with the self they are presenting and respond, either favorably or negatively. Research has shown impression management to be impactful in the workplace because the perceptions co-workers form of one another shape their relationships and indirectly influence their ability to function well as teams and achieve goals together.
In their research on impression management among leaders, Peck and Hogue define "impression management as conscious or unconscious, authentic or inauthentic, goal-directed behavior individuals engage in to influence the impression others form of them in social interactions." Using those three dimensions, labelled "automatic" vs. "controlled", "authentic" vs. "inauthentic", and "pro-self" vs. "pro-social", Peck and Hogue formed a typology of eight impression management archetypes. They suggest that while no one archetype stands out as the sole correct or ideal way to practice impression management as a leader, types rooted in authenticity and pro-social goals, rather than self-focused goals, create the most positive perceptions among followers.
Impression management strategies employed in the workplace also involve deception, and the ability to recognize deceptive acts impacts the supervisor-subordinate relationship as well as coworker relationships. When it comes to workplace behaviors, ingratiation is the major focus of impression management research. Ingratiation behaviors are those that employees engage in to elicit a favorable impression from a supervisor. These behaviors can have a negative or positive impact on coworkers and supervisors, and this impact is dependent on how ingratiating is perceived by the target and those who observe the ingratiating behaviors. The perception that follows an ingratiation act is dependent on whether the target attributes the behavior to the authentic-self of the person performing the act, or to impression management strategies. Once the target is aware that ingratiation is resulting from impression management strategies, the target will perceive ethical concerns regarding the performance. However, if the target attributes the ingratiation performance to the actor's authentic-self, the target will perceive the behavior as positive and not have ethical concerns.
Workplace leaders that are publicly visible, such as CEOs, also perform impression management with regard to stakeholders outside their organizations. In a study comparing online profiles of North American and European CEOs, research showed that while education was referenced similarly in both groups, profiles of European CEOs tended to be more professionally focused, while North American CEO profiles often referenced the CEO's public life outside business dealings, including social and political stances and involvement.
Employees also engage in impression management behaviors to conceal or reveal personal stigmas. How these individuals approach their disclosure of the stigma(s) impacts coworker's perceptions of the individual, as well as the individual's perception of themselves, and thus affects likeability amongst coworkers and supervisors.
On a smaller scale, many individuals choose to participate in professional impression management beyond the sphere of their own workplace. This may take place through informal networking (either face-to-face or using computer-mediated communication) or channels built to connect professionals, such as professional associations, or job-related social media sites, like LinkedIn.
Implications
Impression management can distort the results of empirical research that relies on interviews and surveys, a phenomenon commonly referred to as "social desirability bias". Impression management theory nevertheless constitutes a field of research on its own.
When it comes to practical questions concerning public relations and the way organizations should handle their public image, the assumptions provided by impression management theory can also provide a framework.
An examination of different impression management strategies acted out by individuals who were facing criminal trials where the trial outcomes could range from a death sentence, life in prison or acquittal has been reported in the forensic literature.
The Perri and Lichtenwald article examined female psychopathic killers, whom as a group were highly motivated to manage the impression that attorneys, judges, mental health professions and ultimately, a jury had of the murderers and the murder they committed. It provides legal case illustrations of the murderers combining and/or switching from one impression management strategy such as ingratiation or supplication to another as they worked towards their goal of diminishing or eliminating any accountability for the murders they committed.
Since the 1990s, researchers in the area of sport and exercise psychology have studied self-presentation. Concern about how one is perceived has been found to be relevant to the study of athletic performance. For example, anxiety may be produced when an athlete is in the presence of spectators. Self-presentational concerns have also been found to be relevant to exercise. For example, the concerns may elicit motivation to exercise.
More recent research investigating the effects of impression management on social behaviour showed that social behaviours (e.g. eating) can serve to convey a desired impression to others and enhance one's self-image. Research on eating has shown that people tend to eat less when they believe that they are being observed by others.
See also
Calculating Visions: Kennedy, Johnson, and Civil Rights (book)
Character mask
Dignity
Dramaturgy (sociology)
First impression (psychology)
Ingratiation
Instagram's impact on people
Online identity management
On the Internet, nobody knows you're a dog
Personal branding
Register (sociolinguistics)
Reputation capital
Reputation management
Self-monitoring theory
Self-verification theory
Signalling (economics)
Spin (public relations)
Superficial charm
Stigma management
Footnotes
References
Barnhart, Adam (1994), Erving Goffman: The Presentation of Self in Everyday Life
Goffman, Erving (2006), Wir alle spielen Theater: Die Selbstdarstellung im Alltag, Piper, Munich.
Dillard, Courtney et al. (2000), Impression Management and the use of procedures at the Ritz-Carlton: Moral standards and dramaturgical discipline, Communication Studies, 51.
Döring, Nicola (1999), Sozialpsychologie des Internet: Die Bedeutung des Internet für Kommunikationsprozesse, Identitäten, soziale Beziehungen und Gruppen Hogrefe, Goettingen.
Felson, Richard B (1984): An Interactionist Approach to Aggression, in: Tedeschi, James T. (Ed.), Impression Management Theory and Social Psychological Research Academic Press, New York.
Sanaria, A. D. (2016). A conceptual framework for understanding the impression management strategies used by women in Indian organizations. South Asian Journal of Human Resources Management, 3(1), 25–39. https://doi.org/10.1177/2322093716631118
Hall, Peter (1972). "A Symbolic Interactionist Analysis of Politics." Sociological Inquiry 42.3-4: 35-75
Hass, Glen R. (1981), Presentational Strategies, and the Social Expression of Attitudes: Impression management within Limits, in: Tedeschi, James T. (Ed.): Impression Management Theory and Social Psychological Research, Academic Press, New York.
Humphreys, A. (2016). Social media: Enduring principles. Oxford: Oxford University Press.
Katz, Nathan (2016). "Impression Management, Super PACs and the 2012 Republican Primary." Symbolic Interaction 39.2: 175–95.
Tedeschi, James T.; Riess, Marc (1984), Identities, the Phenomenal Self, and Laboratory Research, in: Tedeschi, James T. (Ed.): Impression Management Theory and Social Psychological Research, Academic Press, New York.
Smith, Greg (2006), Erving Goffman, Routledge, New York.
Rui, J. and M. A. Stefanone (2013). Strategic Management of Other-Provided Information Online: Personality and Network Variables. System Sciences (HICSS), 2013 46th Hawaii International Conference on.
Self
Social influence
Sociology of technology
Reputation management
Majority–minority relations | Impression management | [
"Technology"
] | 9,648 | [
"nan"
] |
601,834 | https://en.wikipedia.org/wiki/Hydrobromic%20acid | Hydrobromic acid is an aqueous solution of hydrogen bromide. It is a strong acid formed by dissolving the diatomic molecule hydrogen bromide (HBr) in water. "Constant boiling" hydrobromic acid is an aqueous solution that distills at and contains 47.6% HBr by mass, which is 8.77 mol/L. Hydrobromic acid is one of the strongest mineral acids known.
Uses
Hydrobromic acid is mainly used for the production of inorganic bromides, especially the bromides of zinc, calcium, and sodium. It is a useful reagent for generating organobromine compounds. Certain ethers are cleaved with HBr. It also catalyzes alkylation reactions and the extraction of certain ores. Industrially significant organic compounds prepared from hydrobromic acid include allyl bromide, tetrabromobis(phenol), and bromoacetic acid. HBr almost uniquely participates in anti-Markovnikov hydrohalogenation of alkenes. The resulting 1-bromoalkanes are versatile alkylating agents, giving rise to fatty amines and quaternary ammonium salts.
Synthesis
Hydrobromic acid can be prepared in the laboratory via the reaction of Br2, SO2, and water.
Br2 + SO2 + 2 H2O -> H2SO4 + 2 HBr
More typically laboratory preparations involve the production of anhydrous HBr, which is then dissolved in water.
Hydrobromic acid has commonly been prepared industrially by reacting bromine with either sulfur or phosphorus and water. However, it can also be produced electrolytically. It can also be prepared by treating bromides with non-oxidising acids like phosphoric or acetic acids.
Alternatively the acid can be prepared with dilute (5.8M) sulfuric acid and potassium bromide:
H2SO4 + KBr -> KHSO4 + HBr
Using more concentrated sulfuric acid or allowing the reaction solution to exceed 75 °C further oxidizes HBr to elemental bromine. The acid is further purified by filtering out the KHSO4 and by distilling off the water until the solution reaches an azeotrope (124.3 °C). The yield is approximately 85%.
Hydrobromic acid is available commercially in various concentrations and purities.
References
External links
International Chemical Safety Card 0282
NIOSH Pocket Guide to Chemical Hazards
Carlin, W. W.
Bromides
Nonmetal halides
Mineral acids
pl:Bromowodór#Kwas bromowodorowy | Hydrobromic acid | [
"Chemistry"
] | 554 | [
"Acids",
"Inorganic compounds",
"Mineral acids",
"Salts",
"Bromides"
] |
601,836 | https://en.wikipedia.org/wiki/Sociosexuality | Sociosexuality, sometimes called sociosexual orientation, is the individual difference in the willingness to engage in sexual activity outside of a committed relationship. Individuals who are more restricted sociosexually are less willing to engage in casual sex; they prefer greater love, commitment and emotional closeness before having sex with romantic partners. Individuals who are more unrestricted sociosexually are more willing to have casual sex and are more comfortable engaging in sex without love, commitment or closeness.
Measurement
The revised Sociosexual Orientation Inventory (SOI-R) was designed to measure sociosexuality, with high SOI scores corresponding to an unrestricted orientation and low SOI scores denoting a more restricted orientation. The SOI-R also allows for the separate assessment of three facets of sociosexuality: behavior, attitude and desire.
Gender differences and sexual orientation
Men tend to have higher SOI scores and be more unrestricted than women across a variety of cultures. However, there is more variability in scores within each gender than between men and women, indicating that although the average man is less restricted than the average woman, individuals may vary in sociosexuality regardless of gender.
Bisexual women are significantly less restricted in their sociosexual attitudes than both lesbian and heterosexual women. Bisexual women are also the most unrestricted in sociosexual behavior, followed by lesbians and then, heterosexual women. Gay and bisexual men are similar to heterosexual men in sociosexual attitudes, in that they express relatively unrestricted attitudes relative to women. However, gay men are the most unrestricted in sociosexual behavior, followed by bisexual men and then, heterosexual men. This may be because gay men have more potential partners who prefer short-term, casual sexual encounters.
Unrestricted sociosexuality is associated with early life experiences with sex, more frequent sexual activity and a greater number of lifetime sex partners. Unrestricted men tend to have greater rape myth acceptance, past sexual aggression and more conservative attitudes about women than restricted men. Unrestricted women tend to have more sexual fantasies involving having power or control over another person and lower levels of sexual conservatism than restricted women.
Individual differences
Individuals who are sociosexually unrestricted tend to score higher on openness to experience, and be more extraverted, less agreeable, lower on honesty-humility, more erotophilic, more impulsive, more likely to take risks, more likely to have an avoidant attachment style, less likely to have a secure attachment style, and score higher on the dark triad traits (i.e. narcissism, Machiavellianism, psychopathy). Higher masculinity and eveningness in women is related to unrestricted sociosexuality. High self-monitoring is also associated with unrestricted sociosexuality, regardless of gender or sexual orientation.
Individuals with an intrinsic religious orientation (i.e., religion as an end) tend to be sociosexually restricted, while those with an extrinsic religious orientation (i.e., religion as a means to achieve non-religious goals) tend to be unrestricted.
Mating tendencies
Motives
Unrestricted women are more motivated to engage in casual sex than restricted women as they perceive more benefits associated with short-term mating. These include sexual benefits (e.g., experiencing the novelty of a new partner), resource benefits (e.g., receiving expensive gifts) and the improvement of their seduction skills. Sociosexuality is not associated with short-term benefits for men.
When viewing attractive female models, unrestricted men are more interested in the models' physical attractiveness, while restricted men show more interest in the social traits presumably possessed by attractive females. Unrestricted women report more interest in attractive male models' popularity and are less interested in their willingness to commit, compared to restricted women.
Mate preferences
Men and women with an unrestricted sociosexual orientation view short-term mates with greater sexual experience as more desirable, whereas restricted women perceive partners' sexual inexperience as desirable. Unrestricted individuals place more importance on partners' physical attractiveness and sex appeal, while restricted individuals place more weight on characteristics indicative of good personal and parenting qualities (e.g., kind, responsible, faithful). Judgement of sexual attractiveness is more variable in unrestricted men than in restricted males.
Individuals are able to accurately assess the sociosexuality of computer-generated and real faces, with unrestricted sociosexuality being associated with greater attractiveness in female faces and greater masculinity in male faces. Women tend to prefer male faces associated with restricted sociosexuality, while men prefer unrestricted female faces, both for short-term and long-term partners.
Relationship interactions
Unrestricted women report engaging in more social interactions with men on a daily basis than restricted women. However, unrestricted individuals rate their interactions with their best friends (non-romantic) as lower in quality (i.e., as less pleasant and satisfying) than restricted individuals. Unrestricted individuals are also more likely to view cheating or infidelity as acceptable under certain conditions (e.g., when involved in a bad relationship), and report engaging in more cheating than restricted individuals. The relationship between sociosexual orientation and infidelity is mediated by commitment, meaning unrestricted individuals may cheat because they are less committed to their partner than restricted individuals.
Hormones
Individuals who are partnered typically have lower testosterone levels than individuals who are single. However, this was found to apply solely to individuals who have a restricted sociosexuality. Partnered, unrestricted men and women's testosterone levels are more similar to the levels of single men and women.
Culture
In regions that suffer from a high prevalence of infectious diseases, both men and women report lower levels of sociosexuality, as the costs of an incautious lifestyle (i.e., being unrestricted) may outweigh the benefits.
Implications
Possessing an unrestricted sociosexuality seems to increase the likelihood of having a son by 12-19% in American samples. This may be explained by the generalized Trivers-Willard hypothesis, which states that parents who possess any heritable trait that increases males' reproductive success above females' will have more sons, and will have more daughters if they possess traits that increase females' reproductive success above males'. Since unrestricted sociosexuality increases the reproductive fitness of sons more than daughters (as males have the potential to have more offspring through casual sex), unrestricted parents have a higher-than-expected offspring sex ratio (more sons).
Relevant theories
Parental investment theory
According to the parental investment theory, the gender that invests more in offspring tends to be more discriminating and more sociosexually restricted (usually women, due to pregnancy, childbirth and lactation). In a year, a woman can give birth once (except in the case of a multiple pregnancy), regardless of the number of partners she has had, whereas a man can potentially have more children than the number of women with whom he has slept due to multiple births. Thus, women should be more selective and restricted in order to have children with partners possessing good genes and resources, who can provide for potential offspring. Men, however, may increase their reproductive fitness by being unrestricted and having many children with many women. Thus, since men do not need to invest as much physically (no pregnancy), they tend to have a more unrestricted sociosexuality.
Sex ratio theory
Operational sex ratio is the number of sexually competing males versus the number of sexually competing females in the local mating pool. High sex ratios indicate that there are more men than women available, while low sex ratios imply more women than men are sexually available. High sex ratios (more men) are associated with lower SOI scores (more restricted sociosexual orientation), as men must satisfy women's preference for long-term monogamous relationships if they are to effectively compete for the limited number of women. Low sex ratios (more women) are correlated with more unrestricted sociosexuality, as men can afford to demand more casual sex if they are relatively scarce and in demand.
Strategic pluralism theory
Strategic pluralism suggests that women evolved to evaluate men on two dimensions: their potential to be a good provider for offspring and their degree of genetic quality. The local environment should have influenced which mate characteristics were preferred by women. In demanding environments where biparental care was critical to infant survival, women should have valued good parenting qualities more, leading men to adopt a more restricted sociosexuality and invest more in their offspring to help ensure their children survive. In disease-prevalent environments, good genes that would help offspring resist pathogens should have been prioritized by women, leading healthy men to be more sociosexually unrestricted in order to pass on their genes to many offspring.
Social structural theory
According to social structural theory, the division of labor and social expectations lead to gender differences in sociosexuality. In cultures with more traditional gender roles (where women have less freedom than men), gender differences in sociosexuality are larger. In these societies, where women have less access to power and money than men, it is expected that women should be more sexually restricted and only have sexual relations with men in the context of a committed relationship, whereas men may be sexually unrestricted if they wish. In more egalitarian societies, where men and women have equal access to power and money, the gender difference in sociosexuality is less pronounced, as individuals may take on the social role of the other gender.
See also
Friends with benefits relationships
Human sexuality
Polyamory
Promiscuity
Sexual arousal
Sexual orientation
References
External links
The revised Sociosexual Orientation Inventory
Sociological terminology
Sexology | Sociosexuality | [
"Biology"
] | 2,018 | [
"Behavioural sciences",
"Behavior",
"Sexology"
] |
601,958 | https://en.wikipedia.org/wiki/Process%20engineering | Process engineering is the understanding and application of the fundamental principles and laws of nature that allow humans to transform raw material and energy into products that are useful to society, at an industrial level. By taking advantage of the driving forces of nature such as pressure, temperature and concentration gradients, as well as the law of conservation of mass, process engineers can develop methods to synthesize and purify large quantities of desired chemical products. Process engineering focuses on the design, operation, control, optimization and intensification of chemical, physical, and biological processes. Their work involves analyzing the chemical makeup of various ingredients and determining how they might react with one another. A process engineer can specialize in a number of areas, including the following:
Agriculture processing
Food and dairy production
Beer and whiskey production
Cosmetics production
Pharmaceutical production
Petrochemical manufacturing
Mineral processing
Printed circuit board production
Overview
Process engineering involves the utilization of multiple tools and methods. Depending on the exact nature of the system, processes need to be simulated and modeled using mathematics and computer science. Processes where phase change and phase equilibria are relevant require analysis using the principles and laws of thermodynamics to quantify changes in energy and efficiency. In contrast, processes that focus on the flow of material and energy as they approach equilibria are best analyzed using the disciplines of fluid mechanics and transport phenomena. Disciplines within the field of mechanics need to be applied in the presence of fluids or porous and dispersed media. Materials engineering principles also need to be applied, when relevant.
Manufacturing in the field of process engineering involves an implementation of process synthesis steps. Regardless of the exact tools required, process engineering is then formatted through the use of a process flow diagram (PFD) where material flow paths, storage equipment (such as tanks and silos), transformations (such as distillation columns, receiver/head tanks, mixing, separations, pumping, etc.) and flowrates are specified, as well as a list of all pipes and conveyors and their contents, material properties such as density, viscosity, particle-size distribution, flowrates, pressures, temperatures, and materials of construction for the piping and unit operations.
The process flow diagram is then used to develop a piping and instrumentation diagram (P&ID) which graphically displays the actual process occurring. P&ID are meant to be more complex and specific than a PFD. They represent a less muddled approach to the design. The P&ID is then used as a basis of design for developing the "system operation guide" or "functional design specification" which outlines the operation of the process. It guides the process through operation of machinery, safety in design, programming and effective communication between engineers.
From the P&ID, a proposed layout (general arrangement) of the process can be shown from an overhead view (plot plan) and a side view (elevation), and other engineering disciplines are involved such as civil engineers for site work (earth moving), foundation design, concrete slab design work, structural steel to support the equipment, etc. All previous work is directed toward defining the scope of the project, then developing a cost estimate to get the design installed, and a schedule to communicate the timing needs for engineering, procurement, fabrication, installation, commissioning, startup, and ongoing production of the process.
Depending on needed accuracy of the cost estimate and schedule that is required, several iterations of designs are generally provided to customers or stakeholders who feed back their requirements. The process engineer incorporates these additional instructions (scope revisions) into the overall design and additional cost estimates, and schedules are developed for funding approval. Following funding approval, the project is executed via project management.
Principal areas of focus in process engineering
Process engineering activities can be divided into the following disciplines:
Process design: synthesis of energy recovery networks, synthesis of distillation systems (azeotropic), synthesis of reactor networks, hierarchical decomposition flowsheets, superstructure optimization, design multiproduct batch plants, design of the production reactors for the production of plutonium, design of nuclear submarines.
Process control: model predictive control, controllability measures, robust control, nonlinear control, statistical process control, process monitoring, thermodynamics-based control, denoted by three essential items, a collection of measurements, method of taking measurements, and a system of controlling the desired measurement.
Process operations: scheduling process networks, multiperiod planning and optimization, data reconciliation, real-time optimization, flexibility measures, fault diagnosis.
Supporting tools: sequential modular simulation, equation-based process simulation, AI/expert systems, large-scale nonlinear programming (NLP), optimization of differential algebraic equations (DAEs), mixed-integer nonlinear programming (MINLP), global optimization, optimization under uncertainty, and quality function deployment (QFD).
Process Economics: This includes using simulation software such as ASPEN, Super-Pro to find out the break even point, net present value, marginal sales, marginal cost, return on investment of the industrial plant after the analysis of the heat and mass transfer of the plant.
Process Data Analytics: Applying data analytics and machine learning methods for process manufacturing problems.
History of process engineering
Various chemical techniques have been used in industrial processes since time immemorial. However, it wasn't until the advent of thermodynamics and the law of conservation of mass in the 1780s that process engineering was properly developed and implemented as its own discipline. The set of knowledge that is now known as process engineering was then forged out of trial and error throughout the industrial revolution.
The term process, as it relates to industry and production, dates back to the 18th century. During this time period, demands for various products began to drastically increase, and process engineers were required to optimize the process in which these products were created.
By 1980, the concept of process engineering emerged from the fact that chemical engineering techniques and practices were being used in a variety of industries. By this time, process engineering had been defined as "the set of knowledge necessary to design, analyze, develop, construct, and operate, in an optimal way, the processes in which the material changes". By the end of the 20th century, process engineering had expanded from chemical engineering-based technologies to other applications, including metallurgical engineering, agricultural engineering, and product engineering.
See also
Chemical process modeling
Chemical technologist
Industrial engineering
Industrial process
Low-gravity process engineering
Materials science
Modular process skid
Process chemistry
Process flowsheeting
Process integration
Systems engineering process
References
External links
Advanced Process Engineering at Cranfield University (Cranfield, UK)
Sargent Centre for Process Systems Engineering (Imperial)
Process Systems Engineering at Cornell University (Ithaca, New York)
Department of Process Engineering at Stellenbosch University
Process Research and Intelligent Systems Modeling (PRISM) group at BYU
Process Systems Engineering at CMU
Process Systems Engineering Laboratory at RWTH Aachen
The Process Systems Engineering Laboratory (MIT)
Process Engineering Consulting at Canada
Process engineering
Engineering disciplines
Chemical processes | Process engineering | [
"Chemistry",
"Engineering"
] | 1,419 | [
"Process engineering",
"Chemical processes",
"Mechanical engineering by discipline",
"nan",
"Chemical process engineering"
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601,983 | https://en.wikipedia.org/wiki/Newcomb%27s%20Tables%20of%20the%20Sun | Newcomb's Tables of the Sun (full title Tables of the Motion of the Earth on its Axis and Around the Sun) is a work by the American astronomer and mathematician Simon Newcomb, published in volume VI of the serial publication Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac. The work contains Newcomb's mathematical development of the position of the Earth in the Solar System, which is constructed from classical celestial mechanics as well as centuries of astronomical measurements. The bulk of the work, however, is a collection of tabulated precomputed values that provide the position of the sun at any point in time.
Newcomb's Tables were the basis for practically all ephemerides of the Sun published from 1900 through 1983, including the annual almanacs of the U.S. Naval Observatory and the Royal Greenwich Observatory. The physical tables themselves were used by the ephemerides from 1900 to 1959, computerized versions were used from 1960 to 1980, and evaluations of the Newcomb's theories were used from 1981 to 1983. The tables are seldom used now; since the Astronomical Almanac for 1984 they have been superseded by more accurate numerically-integrated ephemerides developed at Jet Propulsion Laboratory, based on much more accurate observations than were available to Newcomb. Also, the tables did not account for the effects of general relativity which was unknown at the time. Nevertheless, his tabulated values remain accurate to within a few seconds of arc to this day.
He developed similar formulas and tables for the planets Mercury, Venus, Mars, Uranus and Neptune; those of the inner planets have proved to be the most accurate.
Expressions
Certain expressions have been cited in a number of other works over a long period, and are listed below. Newcomb assigns the symbol T to the time since "1900, Jan. 0, Greenwich Mean noon", measured in Julian centuries of 36,525 days.
Sun's geometric mean longitude
The Sun's geometric mean longitude, freed from aberration is given as
L = 279° 41' 48.04" + " T + 1.089" T2
Authors citing this expression include Borkowski (p. 12) and the Nautical Almanac Offices of the United Kingdom and United States (p. 98).
Fictitious mean Sun
Newcomb gives the Right ascension of the fictitious mean Sun, affected by aberration (which is used in finding mean solar time) as
τ = 18h 38m 45.836s + s T + 0.0929s T2
Authors citing this expression include McCarthy & Seidelmann (p. 13) and the Nautical Almanac Offices of the United Kingdom and United States (p. 73).
Discontinuance
By 1970 the astronomical community recognized the need for improved ephemerides, which are used to prepare national almanacs. The changes required were
a new fundamental catalog of stars to replace FK4
the use of improved values of astronomical constants that had been discovered
a better definition and practical realization of ephemeris time which would take advantage of atomic time
a new epoch to replace 1950.0
It was decided to introduce as many changes as possible at one time in a consistent system, and the new system would go into effect for the 1984 edition of the ephemerides. "The majority of the resolutions were prepared and adopted by the General Assembly of the IAU at the 1976 and 1979 meetings."
The new fundamental ephemeris was prepared by the Jet Propulsion Laboratory and named DE200/LE200. It uses numerical integration.
Notes
References
Works cited
Borkowski, K. M. "The Tropical Year and Solar Calendar". Journal of the Royal Astronomical Society of Canada 85 no. 3 (1990): 121–130.
McCarthy, D. D. & Seidelmann, P. K. TIME from Earth Rotation to Atomic Physics. (Weinheim: Wiley-VCH, 2009).
[U.S.] Nautical Almanac Office and HM Nautical Almanac Office. "The Improved IAU System", a supplement bound with The Astronomical Almanac for the Year 1984. (Washington and London: U.S. Government Printing Office and Her Majesty's Stationery Office, 1983).
Nautical Almanac Offices of the United Kingdom and United States of America. Explanatory Supplement to the Ephemeris. (London: Her Majesty's Stationery Office, 1961).
Newcomb, Simon. Tables of the Four Inner Planets, 2nd ed. (Washington: Bureau of Equipment, Navy Dept., 1898).
Astronomy books | Newcomb's Tables of the Sun | [
"Astronomy"
] | 942 | [
"Astronomy books",
"Works about astronomy"
] |
601,999 | https://en.wikipedia.org/wiki/Assassination%20of%20Luis%20Carrero%20Blanco | On 20 December 1973, Luis Carrero Blanco, the Prime Minister of Spain, was assassinated when a cache of explosives in a tunnel set up by the Basque separatist group ETA was detonated. The assassination, also known by its code name Operación Ogro (Operation Ogre), is considered to have been the biggest attack against the Francoist State since the end of the Spanish Civil War in 1939 and had far-reaching consequences within the politics of Spain.
The death of Carrero Blanco had numerous political implications. By the end of 1973, the physical health of dictator Francisco Franco had declined significantly, and it epitomized the final crisis of the Francoist regime. Following Blanco's death, the most conservative sector of the Francoist State, known as the , wanted to influence Franco so that he would choose an ultraconservative as Prime Minister. Finally, he chose Carlos Arias Navarro, who originally announced a partial relaxation of the most rigid aspects of the Francoist State, but quickly retreated under pressure from the . ETA, on the other hand, consolidated its place as a relevant armed group and would evolve to become one of the main opponents of Francoism.
Assassination
An ETA commando unit using the code name Txikia (after the nom de guerre of ETA activist Eustakio Mendizabal, killed by the Guardia Civil in April 1973) rented a basement flat at Calle Claudio Coello 104, Madrid, on the route by which Blanco regularly went to mass at San Francisco de Borja church.
Over five months, the unit dug a tunnel under the street – telling the landlord that they were student sculptors to hide their true purpose. The tunnel was packed with of Goma-2 that had been stolen from a government depot.
On 20 December at 9:36 am, a three-man ETA commando unit disguised as electricians detonated the explosives by command wire as Blanco's Dodge Dart passed. The blast sent Blanco and his car into the air and over the five-story church, landing on the second-floor terrace of the opposite side. Blanco survived the blast but died at 10:15 am in hospital. His bodyguard and driver died shortly afterwards. The "electricians" shouted to stunned passers-by that there had been a gas explosion, and then fled in the confusion. ETA claimed responsibility on 22 January 1974.
In a collective interview justifying the attack, the ETA bombers said:
The killing was not condemned and was, in some cases, even welcomed by the Spanish opposition in exile. According to Laura Desfor Edles, professor of sociology at California State University, Northridge, some analysts consider the assassination of Carrero Blanco to be the only thing the ETA have ever done to "further the cause of Spanish democracy". However, former ETA member turned writer Jon Juaristi contended that ETA's goal with the killing was not democratization but a spiral of violence to fully destabilize Spain, heighten Franco's repression against Basque nationalism and force the average Basque citizen to support the lesser evil in the form of the ETA against Franco.
According to colonel Amadeo Martínez Inglés, it was planned, organized and carried out by CIA, for its similarities with the assassination of René Schneider, with the collaboration of ETA.
Reaction
A government meeting about the "dangers of subversion threatening Spain" was scheduled to take place on 20 December 1973. Both Carrero Blanco and the United States Secretary of State, Henry Kissinger, had expressed concern about a left-wing uprising during the meeting they held on 19 December. When government officials reached the Palace of Villamejor, they learned about Carrero Blanco's death. Deputy Prime Minister Torcuato Fernández Miranda demanded calm and announced that he was going to call Franco so that Franco could decide what to do next. After the call, Fernández Miranda proclaimed himself prime minister, in accordance with the dispositions laid out in the Organic Law of the State. His first decision as prime minister was to decline to declare a state of exception.
Gabriel Pita da Veiga, Minister of the Navy, informed Fernández Miranda that Carlos Iniesta Cano, Director-General of the Civil Guard, had decided to "maximize surveillance" and ordered agents through a telegram not to hesitate to use deadly force if any clash occurred. However, Fernández Miranda was opposed and made Iniesta Cano reverse this order immediately through a telegram.
See also
Cassandra case, student prosecuted for posting a series of tweets poking fun at the assassination of Luis Carrero Blanco
Operación Ogro, a film about the attack by Gillo Pontecorvo
The Last Circus, a film where the attack is a minor part of the plot
References
Terrorist incidents in Spain in the 1970s
1970s in Madrid
1973 murders in Spain
Assassinations in Spain
Deaths by person in Spain
Francoist Spain
Terrorist incidents in Europe in 1973
ETA (separatist group) actions
Tunnel warfare
Improvised explosive device bombings in Madrid
Improvised explosive device bombings in 1973
1973 in politics | Assassination of Luis Carrero Blanco | [
"Engineering"
] | 1,012 | [
"Military engineering",
"Tunnel warfare"
] |
602,014 | https://en.wikipedia.org/wiki/Laptop%20theft | Laptop theft (or notebook theft) is a significant threat to users of laptop computers. Many methods to protect the data and to prevent theft have been developed, including alarms, laptop locks, and visual deterrents such as stickers or labels. Victims of laptop theft can lose hardware, software, and essential data that has not been backed up. Thieves also may have access to sensitive data and personal information. Some systems authorize access based on credentials stored on the laptop including MAC addresses, web cookies, cryptographic keys and stored passwords.
According to the FBI, losses due to laptop theft totaled more than $3.5 million in 2005. The Computer Security Institute/FBI Computer Crime & Security Survey found the average theft of a laptop to cost a company $31,975. In a study surveying 329 private and public organizations published by Intel in 2010, 7.1% of employee laptops were lost or stolen before the end of their usefulness lifespan. Furthermore, it was determined that the average total negative economic impact of a stolen laptop was $49,256—primarily due to compromised data, and efforts to retroactively protect organizations and people from the potential consequences of that compromised data. The total cost of lost laptops to all organizations involved in the study was estimated at $2.1 billion. Of the $48B lost from the U.S. economy as a result of data breaches, 28% resulted from stolen laptops or other portable devices.
In the 2011, Bureau Brief prepared by the NSW Bureau of Crime Statistics and Research it was reported that thefts of laptops have been on the increase over the last 10 years, attributed in part by an increase in ownership but also because they are an attractive proposition for thieves and opportunists. In 2001 2,907 laptops were stolen from New South Wales dwellings, but by 2010 this had risen to 6,492, second only to cash of items taken by thieves. The Bureau reports that one in four break-ins in 2010 resulted in a laptop being stolen. This startling trend in burglaries lends itself to an increase in identity theft and fraud due to the personal and financial information commonly found on laptops. These statistics do not take into account unreported losses so the figures could arguably be much higher.
Businesses have much to lose if an unencrypted or poorly secured laptop is misappropriated, yet many do not adequately assess this risk and take appropriate action. Loss of sensitive company information is of significant risk to all businesses and measures should be taken to adequately protect this data. A survey conducted in multiple countries suggested that employees are often careless or deliberately circumvent security procedures, which leads to the loss of the laptop. According to the survey, employees were most likely to lose a laptop while travelling at hotels, airports, rental cars, and conference events.
Behling and Wood examined the issue of laptop security and theft. Their survey of employees in southern New England highlighted that not only were security measures fundamentally basic but that training employees in security measures was limited and inadequate.
100% of the surveyed employees had access to company information via a laptop from remote sites that included their own homes.
78% were authorized to store company data on their laptop.
36% of businesses did not provide security training.
They concluded that trends in laptop thefts needed to be monitored to assess what intervention measures were required.
Inside protection
Passwords are no longer adequate to protect laptops. There are many solutions that can improve the strength of a laptop's protection. Full disk encryption (FDE) is an increasingly popular and cost-effective approach. FDE can be taken on from a software-based approach, a hardware-based approach, or both-end-based approach. FDE provides protection before the operating system starts up with pre-boot authentication, however precautions still need to be taken against cold boot attacks.
There are a number of tools available, both commercial and open source that enable a user to circumvent passwords for Windows, Mac OS X, and Linux. One example is TrueCrypt which allows users to create a virtual encrypted disk on their computer.
Passwords provide a basic security measure for files stored on a laptop, though combined with disk encryption software they can reliably protect data against unauthorized access. Remote Laptop Security (RLS) is available to confidently secure data even when the laptop is not in the owner's possession. With Remote Laptop Security, the owner of a laptop can deny access rights to the stolen laptop from any computer with Internet access.
Physical protection
A number of computer security measures have emerged that aim at protecting data. The Kensington Security Slot along with a locking cable provides physical security against thefts of opportunity. This is a cord that is attached to something heavy that cannot be moved, and is then locked into the case of the laptop, but this is not 100% secure.
The Noble security lock slot is a different way to attach a security cable.
Centralization of laptop data
Another possible approach to limiting the consequences of laptop theft is to issue thin client devices to field employees instead of conventional laptops, so that all data will reside on the server and therefore may be less liable to loss or compromise. If a thin client is lost or stolen, it can easily and inexpensively be replaced. However, a thin client depends on network access to the server, which is not available aboard airliners or any other location without network access.
This approach can be coupled with strong authentication as such single sign-on (SSO).
Major laptop thefts
In 2006 a laptop in custody of a data analyst was stolen that contained personal and health data of about 26.5 million active duty troops and veterans. The agency has estimated that it will cost between $100 million to $500 million to prevent and cover possible losses from the data theft. In 2007, the United States Department of Veterans Affairs agreed to pay $20 million to current and former military personnel to settle a class action lawsuit.
In 2007 the Financial Services Authority (FSA) fined the UK's largest building society, Nationwide, £980,000 for inadequate procedures when an employee's laptop was stolen during a domestic burglary. The laptop had details of 11 million customers' names and account numbers and, whilst the device was password protected, the information was unencrypted. The FSA noted that the systems and controls fell short, given that it took the Nationwide three weeks to take any steps to investigate the content on the missing laptop. The substantial fine was invoked to reinforce the FSA's commitment to reducing financial crime.
In 2010 VA reported the theft of the laptop from an unidentified contractor; the computer contained personally identifiable information on 644 veterans, including data from some VA medical centers' records.
After learning about the unencrypted laptop, VA investigated how many VA contractors might not be complying with the encryption requirement and learned that 578 vendors had refused to sign new contract clauses that required them to encrypt veteran data on their computers, an apparent violation of rules.
Common locations
LoJack for Laptops has compiled a list of the top ten places from which laptops are stolen:
Public Schools (K–12)
Residential Properties
Automobiles (excluding taxis)
Businesses/Offices
Universities and Colleges
Restaurants and Cafes
Hotels and Motels
Dormitory
Airports
Public Transit (taxi, bus, train)
To provide some context, the Ponemon Institute released a study that indicates over 600,000 laptops will be lost or stolen at US airports every year, with 65–69% of them remaining unclaimed.
See also
Device tracking software
IT risk
Pre-boot authentication
Prey (software)
References
External links
The spy who lost me - laptop thefts from the British Ministry of Defence
2005 CSI/FBI Computer Crime and Security Survey - statistics and information about computer crime
Computer security exploits
Theft
Theft | Laptop theft | [
"Technology"
] | 1,598 | [
"Computer security exploits"
] |
602,016 | https://en.wikipedia.org/wiki/TreadMarks | TreadMarks is a distributed shared memory system created at Rice University in the 1990s.
References
External links
TreadMarks official site
Distributed computing architecture | TreadMarks | [
"Technology",
"Engineering"
] | 28 | [
"Computing stubs",
"Computer engineering stubs",
"Computer engineering"
] |
602,032 | https://en.wikipedia.org/wiki/Pierre%20Janssen | Pierre Jules César Janssen (22 February 1824 – 23 December 1907), usually known as Jules Janssen, was a French astronomer who, along with English scientist Joseph Norman Lockyer, is credited with discovering the gaseous nature of the solar chromosphere, but there is no justification for the conclusion that he deserves credit for the co-discovery of the element helium.
Life, work, and interests
Janssen was born in Paris (During Bourbon Restoration in France) into a cultivated family. His father, César Antoine Janssen (born in Paris, 1780 – 1860) was a well known clarinettist from Dutch/Belgian descent (his father, Christianus Janssen, emigrated from Walloon Brabant to Paris). His mother Pauline Marie Le Moyne (1789 – 1871) was a daughter of the architect Paul Guillaume Le Moyne.
Pierre Janssen studied mathematics and physics at the faculty of sciences. He taught at the Lycée Charlemagne in 1853, and in the school of architecture 1865 – 1871, but his energies were mainly devoted to various scientific missions entrusted to him. Thus in 1857 he went to Peru in order to determine the magnetic equator; in 1861–1862 and 1864, he studied telluric absorption in the solar spectrum in Italy and Switzerland; in 1867 he carried out optical and magnetic experiments at the Azores; he successfully observed both transits of Venus, that of 1874 in Japan, that of 1882 at Oran in Algeria; and he took part in a long series of solar eclipse-expeditions, e.g. to Trani, Italy (1867), Guntur, India (1868), Algiers (1870), Siam (1875), the Caroline Islands (1883), and to Alcossebre in Spain (1905). To see the eclipse of 1870, he escaped from the Siege of Paris in a balloon. Unfortunately the eclipse was obscured from him by cloud.
In the year 1874, Janssen invented the Revolver of Janssen or Photographic Revolver, instrument that originated the chronophotography. Later this invention was of great use for researchers like Etienne Jules Marey to carry out exhibitions and inventions.
Solar spectroscopy
In 1868 Janssen discovered how to observe solar prominences without an eclipse. While observing the solar eclipse of 18 August 1868, at Guntur, Madras State (now in Andhra Pradesh), British India, he noticed bright lines in the spectrum of the chromosphere, showing that the chromosphere is gaseous. From the brightness of the spectral lines, Janssen realized that the chromospheric spectrum could be observed even without an eclipse, and he proceeded to do so. But he never mentioned the emission line seen by Joseph Norman Lockyer, which later was shown to be due to the element helium.
On 20 October, Lockyer in England set up a new, relatively powerful spectroscope. He also observed the emission spectrum of the chromosphere, including a new yellow line near the sodium D line, which he called "D3". Lockyer and the English chemist Edward Frankland speculated that the new line could be due to a new element, which they named the element after the Greek word for the Sun, ἥλιος (helios).
Observatories
At the great Indian eclipse of 1868 that occurred in Guntur, Janssen also demonstrated the gaseous nature of the red prominences, and devised a method of observing them under ordinary daylight conditions. One main purpose of his spectroscopic inquiries was to answer the question whether the Sun contains oxygen or not. An indispensable preliminary was the virtual elimination of oxygen-absorption in the Earth's atmosphere, and his bold project of establishing an observatory on the top of Mont Blanc was prompted by a perception of the advantages to be gained by reducing the thickness of air through which observations have to be made. This observatory, the foundations of which were fixed in the hard ice that appeared to cover the summit to a depth of over ten metres, was built in September 1893, and Janssen, in spite of his sixty-nine years, made the ascent and spent four days making observations.
In 1875, Janssen was appointed director of the new astrophysical observatory established by the French government at Meudon, and set on foot there in 1876 the remarkable series of solar photographs collected in his great Atlas de photographies solaires (1904). The first volume of the Annales de l'observatoire de Meudon was published by him in 1896. (see also Meudon Great Refractor)
Janssen was the President of the Société Astronomique de France (SAF), the French astronomical society, from 1895 to 1897.
International Meridian Conference
In 1884 he took part in the International Meridian Conference.
Death, honors, and legacy
Janssen died at Meudon on 23 December 1907 and was buried at Père Lachaise Cemetery in Paris, with the name "J. Janssen" inscribed on his tomb. During his life he was made a Knight of the Legion of Honor and a Foreign Member of the Royal Society of London.
Craters on both Mars and the Moon are named in his honor. The public square in front of Meudon Observatory is named Place Jules Janssen after him. Two major prizes carry his name: the Prix Jules Janssen of the French Astronomical Society, and the Janssen Medal of the French Academy of Sciences.
Janssen named minor planet 225 Henrietta discovered by Johann Palisa, after his wife, Henrietta.
Notes and references
Further reading
Obituary, from Popular Astronomy, 1908, vol. 16, pp. 72–74
Obituary, from Astronomische Nachrichten, 1908, vol. 177, p. 63 (in French)
Obituary, from The Astrophysical Journal, 1908, vol. 28, pp. 89–99 (in French)
Janssen statue, description and black-and-white picture from The Observatory, 1922, vol. 45, pp. 175–176
Brief biography, from the High Altitude Observatory at Boulder, Colorado
1824 births
1907 deaths
Burials at Père Lachaise Cemetery
Discoverers of chemical elements
19th-century French astronomers
Members of the French Academy of Sciences
Foreign members of the Royal Society
Foreign associates of the National Academy of Sciences
Knights of the Legion of Honour
Honorary Fellows of the Royal Society of Edinburgh
Scientists from Paris
Helium
Spectroscopists
Recipients of the Lalande Prize
Articles containing video clips
French people of Belgian descent | Pierre Janssen | [
"Physics",
"Chemistry"
] | 1,303 | [
"Physical chemists",
"Spectrum (physical sciences)",
"Analytical chemists",
"Spectroscopists",
"Spectroscopy"
] |
602,264 | https://en.wikipedia.org/wiki/LC%20circuit | An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can act as an electrical resonator, an electrical analogue of a tuning fork, storing energy oscillating at the circuit's resonant frequency.
LC circuits are used either for generating signals at a particular frequency, or picking out a signal at a particular frequency from a more complex signal; this function is called a bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners and frequency mixers.
An LC circuit is an idealized model since it assumes there is no dissipation of energy due to resistance. Any practical implementation of an LC circuit will always include loss resulting from small but non-zero resistance within the components and connecting wires. The purpose of an LC circuit is usually to oscillate with minimal damping, so the resistance is made as low as possible. While no practical circuit is without losses, it is nonetheless instructive to study this ideal form of the circuit to gain understanding and physical intuition. For a circuit model incorporating resistance, see RLC circuit.
Terminology
The two-element LC circuit described above is the simplest type of inductor-capacitor network (or LC network). It is also referred to as a second order LC circuit to distinguish it from more complicated (higher order) LC networks with more inductors and capacitors. Such LC networks with more than two reactances may have more than one resonant frequency.
The order of the network is the order of the rational function describing the network in the complex frequency variable . Generally, the order is equal to the number of L and C elements in the circuit and in any event cannot exceed this number.
Operation
An LC circuit, oscillating at its natural resonant frequency, can store electrical energy. See the animation. A capacitor stores energy in the electric field () between its plates, depending on the voltage across it, and an inductor stores energy in its magnetic field (), depending on the current through it.
If an inductor is connected across a charged capacitor, the voltage across the capacitor will drive a current through the inductor, building up a magnetic field around it. The voltage across the capacitor falls to zero as the charge is used up by the current flow. At this point, the energy stored in the coil's magnetic field induces a voltage across the coil, because inductors oppose changes in current. This induced voltage causes a current to begin to recharge the capacitor with a voltage of opposite polarity to its original charge. Due to Faraday's law, the EMF which drives the current is caused by a decrease in the magnetic field, thus the energy required to charge the capacitor is extracted from the magnetic field. When the magnetic field is completely dissipated the current will stop and the charge will again be stored in the capacitor, with the opposite polarity as before. Then the cycle will begin again, with the current flowing in the opposite direction through the inductor.
The charge flows back and forth between the plates of the capacitor, through the inductor. The energy oscillates back and forth between the capacitor and the inductor until (if not replenished from an external circuit) internal resistance makes the oscillations die out. The tuned circuit's action, known mathematically as a harmonic oscillator, is similar to a pendulum swinging back and forth, or water sloshing back and forth in a tank; for this reason the circuit is also called a tank circuit. The natural frequency (that is, the frequency at which it will oscillate when isolated from any other system, as described above) is determined by the capacitance and inductance values. In most applications the tuned circuit is part of a larger circuit which applies alternating current to it, driving continuous oscillations. If the frequency of the applied current is the circuit's natural resonant frequency (natural frequency below), resonance will occur, and a small driving current can excite large amplitude oscillating voltages and currents. In typical tuned circuits in electronic equipment the oscillations are very fast, from thousands to billions of times per second.
Resonance effect
Resonance occurs when an LC circuit is driven from an external source at an angular frequency at which the inductive and capacitive reactances are equal in magnitude. The frequency at which this equality holds for the particular circuit is called the resonant frequency. The resonant frequency of the LC circuit is
where is the inductance in henries, and is the capacitance in farads. The angular frequency has units of radians per second.
The equivalent frequency in units of hertz is
Applications
The resonance effect of the LC circuit has many important applications in signal processing and communications systems.
The most common application of tank circuits is tuning radio transmitters and receivers. For example, when tuning a radio to a particular station, the LC circuits are set at resonance for that particular carrier frequency.
A series resonant circuit provides voltage magnification.
A parallel resonant circuit provides current magnification.
A parallel resonant circuit can be used as load impedance in output circuits of RF amplifiers. Due to high impedance, the gain of amplifier is maximum at resonant frequency.
Both parallel and series resonant circuits are used in induction heating.
LC circuits behave as electronic resonators, which are a key component in many applications:
Amplifiers
Oscillators
Filters
Tuners
Mixers
Foster–Seeley discriminator
Contactless cards
Graphics tablets
Electronic article surveillance (security tags)
Time domain solution
Kirchhoff's laws
By Kirchhoff's voltage law, the voltage across the capacitor plus the voltage across the inductor must equal zero:
Likewise, by Kirchhoff's current law, the current through the capacitor equals the current through the inductor:
From the constitutive relations for the circuit elements, we also know that
Differential equation
Rearranging and substituting gives the second order differential equation
The parameter , the resonant angular frequency, is defined as
Using this can simplify the differential equation:
The associated Laplace transform is
thus
where is the imaginary unit.
Solution
Thus, the complete solution to the differential equation is
and can be solved for and by considering the initial conditions. Since the exponential is complex, the solution represents a sinusoidal alternating current. Since the electric current is a physical quantity, it must be real-valued. As a result, it can be shown that the constants and must be complex conjugates:
Now let
Therefore,
Next, we can use Euler's formula to obtain a real sinusoid with amplitude , angular frequency , and phase angle .
Thus, the resulting solution becomes
Initial conditions
The initial conditions that would satisfy this result are
Series circuit
In the series configuration of the LC circuit, the inductor (L) and capacitor (C) are connected in series, as shown here. The total voltage across the open terminals is simply the sum of the voltage across the inductor and the voltage across the capacitor. The current into the positive terminal of the circuit is equal to the current through both the capacitor and the inductor.
Resonance
Inductive reactance increases as frequency increases, while capacitive reactance decreases with increase in frequency (defined here as a positive number). At one particular frequency, these two reactances are equal and the voltages across them are equal and opposite in sign; that frequency is called the resonant frequency for the given circuit.
Hence, at resonance,
Solving for , we have
which is defined as the resonant angular frequency of the circuit. Converting angular frequency (in radians per second) into frequency (in Hertz), one has
and
at .
In a series configuration, and cancel each other out. In real, rather than idealised, components, the current is opposed, mostly by the resistance of the coil windings. Thus, the current supplied to a series resonant circuit is maximal at resonance.
In the limit as current is maximal. Circuit impedance is minimal. In this state, a circuit is called an acceptor circuit
For , ; hence, the circuit is capacitive.
For , ; hence, the circuit is inductive.
Impedance
In the series configuration, resonance occurs when the complex electrical impedance of the circuit approaches zero.
First consider the impedance of the series LC circuit. The total impedance is given by the sum of the inductive and capacitive impedances:
Writing the inductive impedance as and capacitive impedance as and substituting gives
Writing this expression under a common denominator gives
Finally, defining the natural angular frequency as
the impedance becomes
where gives the reactance of the inductor at resonance.
The numerator implies that in the limit as , the total impedance will be zero and otherwise non-zero. Therefore the series LC circuit, when connected in series with a load, will act as a band-pass filter having zero impedance at the resonant frequency of the LC circuit.
Parallel circuit
When the inductor (L) and capacitor (C) are connected in parallel as shown here, the voltage across the open terminals is equal to both the voltage across the inductor and the voltage across the capacitor. The total current flowing into the positive terminal of the circuit is equal to the sum of the current flowing through the inductor and the current flowing through the capacitor:
Resonance
When equals , the two branch currents are equal and opposite. They cancel each other out to give minimal current in the main line (in principle, for a finite voltage , there is zero current). Since total current in the main line is minimal, in this state the total impedance is maximal. There is also a larger current circulating in the loop formed by the capacitor and inductor. For a finite voltage , this circulating current is finite, with value given by the respective voltage-current relationships of the capacitor and inductor. However, for a finite total current in the main line, in principle, the circulating current would be infinite. In reality, the circulating current in this case is limited by resistance in the circuit, particularly resistance in the inductor windings.
The resonant frequency is given by
Any branch current is not minimal at resonance, but each is given separately by dividing source voltage () by reactance (). Hence , as per Ohm's law.
At , the line current is minimal. The total impedance is maximal. In this state a circuit is called a rejector circuit.
Below , the circuit is inductive.
Above , the circuit is capacitive.
Impedance
The same analysis may be applied to the parallel LC circuit. The total impedance is then given by
and after substitution of and and simplification, gives
Using
it further simplifies to
Note that
but for all other values of the impedance is finite.
Thus, the parallel LC circuit connected in series with a load will act as band-stop filter having infinite impedance at the resonant frequency of the LC circuit, while the parallel LC circuit connected in parallel with a load will act as band-pass filter.
Laplace solution
The LC circuit can be solved using the Laplace transform.
We begin by defining the relation between current and voltage across the capacitor and inductor in the usual way:
and
Then by application of Kirchhoff's laws, we may arrive at the system's governing differential equations
With initial conditions and
Making the following definitions,
and
gives
Now we apply the Laplace transform.
The Laplace transform has turned our differential equation into an algebraic equation. Solving for in the domain (frequency domain) is much simpler viz.
Which can be transformed back to the time domain via the inverse Laplace transform:
For the second summand, an equivalent fraction of is needed:
For the second summand, an equivalent fraction of is needed:
The final term is dependent on the exact form of the input voltage. Two common cases are the Heaviside step function and a sine wave. For a Heaviside step function we get
For the case of a sinusoidal function as input we get:
where is the amplitude and the frequency of the applied function.
Using the partial fraction method:
Simplifiying on both sides
We solve the equation for A, B and C:
Substitute the values of A, B and C:
Isolating the constant and using equivalent fractions to adjust for lack of numerator:
Performing the reverse Laplace transform on each summands:
Using initial conditions in the Laplace solution:
History
The first evidence that a capacitor and inductor could produce electrical oscillations was discovered in 1826 by French scientist Felix Savary. He found that when a Leyden jar was discharged through a wire wound around an iron needle, sometimes the needle was left magnetized in one direction and sometimes in the opposite direction. He correctly deduced that this was caused by a damped oscillating discharge current in the wire, which reversed the magnetization of the needle back and forth until it was too small to have an effect, leaving the needle magnetized in a random direction. American physicist Joseph Henry repeated Savary's experiment in 1842 and came to the same conclusion, apparently independently.
Irish scientist William Thomson (Lord Kelvin) in 1853 showed mathematically that the discharge of a Leyden jar through an inductance should be oscillatory, and derived its resonant frequency. British radio researcher Oliver Lodge, by discharging a large battery of Leyden jars through a long wire, created a tuned circuit with its resonant frequency in the audio range, which produced a musical tone from the spark when it was discharged. In 1857, German physicist Berend Wilhelm Feddersen photographed the spark produced by a resonant Leyden jar circuit in a rotating mirror, providing visible evidence of the oscillations. In 1868, Scottish physicist James Clerk Maxwell calculated the effect of applying an alternating current to a circuit with inductance and capacitance, showing that the response is maximum at the resonant frequency. The first example of an electrical resonance curve was published in 1887 by German physicist Heinrich Hertz in his pioneering paper on the discovery of radio waves, showing the length of spark obtainable from his spark-gap LC resonator detectors as a function of frequency.
One of the first demonstrations of resonance between tuned circuits was Lodge's "syntonic jars" experiment around 1889. He placed two resonant circuits next to each other, each consisting of a Leyden jar connected to an adjustable one-turn coil with a spark gap. When a high voltage from an induction coil was applied to one tuned circuit, creating sparks and thus oscillating currents, sparks were excited in the other tuned circuit only when the circuits were adjusted to resonance. Lodge and some English scientists preferred the term "syntony" for this effect, but the term "resonance" eventually stuck. The first practical use for LC circuits was in the 1890s in spark-gap radio transmitters to allow the receiver and transmitter to be tuned to the same frequency. The first patent for a radio system that allowed tuning was filed by Lodge in 1897, although the first practical systems were invented in 1900 by Italian radio pioneer Guglielmo Marconi.
See also
RL circuit
RC circuit
RLC circuit
References
External links
An electric pendulum by Tony Kuphaldt is a classical story about the operation of LC tank
How the parallel-LC circuit stores energy is another excellent LC resource.
Analog circuits
Electronic filter topology
History of radio technology
Linear electronic circuits | LC circuit | [
"Engineering"
] | 3,310 | [
"Analog circuits",
"Electronic engineering"
] |
602,386 | https://en.wikipedia.org/wiki/Try%20square | A try square or try-square is a woodworking tool used for marking and checking 90° angles on pieces of wood. Though woodworkers use many different types of square, the try square is considered one of the essential tools for woodworking.
The square in the name refers to the 90° angle. To try a piece of wood is to check if the edges and faces are straight, flat, and square to one another. A try square is so called because it is used to try how square the workpiece is.
Description
A try square is made of two key parts, the blade (also known as a beam or tongue) and the stock, which are fixed together at 90° to form an 'L' shape.
The blade is usually made of wood or steel and is fixed into the stock, which is usually thicker than the blade and made of wood, metal or plastic. Both the stock and the tongue are usually made with parallel edges. Typically the blade and the stock will be rectangular in profile, though on some wooden squares the ends of the blade and the stock might be cut to a decorative shape. Some steel blades also have ruler markings for making measurements.
Often the top of the stock will not cover the full width of the blade so the stock does not get in the way when making a mark. This gap also allows space should an inaccurate blade need to be planed, filed or sanded.
Try squares are typically long. squares are handier for small tasks that don't require a longer square, such as marking small joints. A typical general purpose square is . Larger squares are used for tasks such as cabinetry, and are more likely to be made by the woodworker themselves, but other methods are often preferred for such larger tasks.
A common form of try square has a broad blade made of steel that is riveted into a stable, dense tropical hardwood stock, often ebony or rosewood. The inside of the wooden stock usually has a brass strip fixed to it to reduce wear.
On some squares the top of the stock is angled at 45°, so the square can be used as a mitre square for marking and checking 45° angles.
A similar type of square is the engineer's square, used in metalworking and by some woodworkers. The blade is made with both a steel blade and a steel stock and is usually manufactured to a higher degree of accuracy.
Use
The stock is usually held against the edge of the workpiece and either side of the tongue is then used as a straight edge for making a mark, or as a reference to check the accuracy of an angle.
When checking if an angle is square, the woodworker will test the workpiece in multiple places or will run the square along the length of the workpiece. The woodworker might hold the workpiece up towards a light to help see any gaps between the workpiece and the square. Another method is to try sliding feeler gauges between the square and the workpiece.
For making a mark a woodworker might use a pencil, a pen or, for greater accuracy, a marking knife or blade.
History and symbolism
Wooden try squares have survived from Ancient Egypt and Ancient Rome and can be seen in art from the time. From the 18th century squares began to be manufactured in factories, prior to that they were typically made from wood and made by the tradesmen themselves. Some woodworkers continue to make their own try squares.
The square is incorporated into the most common Freemasonry symbol, the Square and Compasses. Historically squares have also been used by woodworkers, such as joiners and carpenters, as symbols in signs and heraldry to represent their trade. The square as a symbol is also seen in artistic representations of the Christian saints Thomas the Apostle and James the Less.
Accuracy
A square can become less accurate over time through both common use and abuse, such as the edges becoming worn over time or the square being dropped or mistreated. Wooden squares can also vary with changes in temperature and humidity. For this reason more dimensionally stable woods, such as mahogany, are preferred.
There are a number of methods for correcting an inaccurate square by hand. Wooden blades can be corrected using a hand plane and sandpaper, while metal blades can be corrected using a file, emery cloth, or sandpaper.
See also
Combination square
Machinist square
Set square
Steel square
Speed square
Square (tool)
References
Dimensional instruments
Woodworking measuring instruments
Squares (tool) | Try square | [
"Physics",
"Mathematics"
] | 910 | [
"Quantity",
"Dimensional instruments",
"Physical quantities",
"Size"
] |
602,388 | https://en.wikipedia.org/wiki/John%20McAfee | John David McAfee ( ; 18 September 1945 – 23 June 2021) was a British and American computer programmer, businessman, and two-time presidential candidate who unsuccessfully sought the Libertarian Party nomination for president of the United States in 2016 and in 2020. In 1987, he wrote the first commercial anti-virus software, founding McAfee Associates to sell his creation. He resigned in 1994 and sold his remaining stake in the company. McAfee became the company's most vocal critic in later years, urging consumers to uninstall the company's anti-virus software, which he characterized as bloatware. He disavowed the company's continued use of his name in branding, a practice that has persisted in spite of a short-lived corporate rebrand attempt under Intel ownership.
McAfee's fortunes plummeted in the financial crisis of 2007–2008. After leaving McAfee Associates, he founded the companies Tribal Voice (makers of the PowWow chat program), QuorumEx, and Future Tense Central, among others, and was involved in leadership positions in the companies Everykey, MGT Capital Investments, and Luxcore, among others. His personal and business interests included smartphone apps, cryptocurrency, yoga, light-sport aircraft and recreational drug use. He resided for a number of years in Belize, but returned to the United States in 2013 while wanted in Belize for questioning on suspicion of murder.
McAfee was a vocal advocate for privacy and personal freedom, central to his libertarian campaigns in 2016 and 2020. He opposed government surveillance and supported cryptocurrency as a way to reduce state control over financial systems. He framed his legal issues, including tax evasion charges, as resistance to unjust government overreach.
In October 2020, McAfee was arrested in Spain over U.S. tax evasion charges. U.S. federal prosecutors brought criminal and civil charges alleging that McAfee had failed to file income taxes over a four-year period. On 23 June 2021, he was found dead due to an apparent suicide by hanging in his prison cell near Barcelona shortly after the Spanish National Court authorized his extradition to the U.S. His death generated speculation and theories about the possibility that he was murdered. McAfee's wife, Janice McAfee, said she did not believe McAfee died by suicide.
Early life
McAfee was born in Cinderford, in the Forest of Dean, Gloucestershire, England, on 18 September 1945, on a U.S. Army base (of the 596th Ordnance Ammunition Company), to an American father, Don McAfee, who was stationed there, and a British mother, Joan Williams. His father was from Roanoke, Virginia. In spite of primarily being raised in Salem, Virginia, McAfee said he felt as much British as American. When he was 15, his father, whom a BBC columnist described as "an abusive alcoholic", killed himself with a gun. He had spent his childhood living in fear that a beating from his father could happen at any time and struggled to make sense of why this was happening to him. In Running With the Devil: The Wild World of John McAfee, it is alleged that McAfee may have shot and killed his father, staging the scene to look like a suicide.
McAfee received a bachelor's degree in mathematics in 1967 from Roanoke College in Virginia, which subsequently awarded him an honorary Doctor of Science degree in 2008. After receiving his bachelor's degree, McAfee began working towards a doctorate in mathematics at Northeast Louisiana State College, but was expelled in about 1968 because of a relationship with an undergraduate student, who became his first wife.
Ventures
NASA, Univac, Xerox, CSC, Booz Allen and Lockheed
McAfee was employed as a programmer by NASA from 1968 to 1970. From there, he went to Univac as a software designer, and later to Xerox as an operating system architect. In 1978, he joined Computer Sciences Corporation as a software consultant. He worked for consulting firm Booz Allen Hamilton from 1980 to 1982. In 1986, while employed by Lockheed, he read about the Brain computer virus made for the PC, and he found it terrifying. Sensing a business opportunity, he went about creating an antivirus software that could detect the computer virus and remove it automatically. In 1987, McAfee created McAfee Associates Inc. to sell this software, which he named VirusScan. This was the first anti-virus software brought to market, and one of the first software products to be distributed over the Internet.
McAfee Associates
Initially McAfee did not seek a large userbase of paying users, but rather wanted to raise awareness of the need to be protected from computer viruses. However, by making people fear such malware, he managed to generate millions of sales, and by 1990 he was making $5 million a year. The company was incorporated in Delaware in 1992, and had its initial public offering the same year. In August 1993, McAfee stepped down as chief executive and remained with the company as the chief technical officer. He was succeeded by Bill Larson. In 1994 he sold his remaining stake in the company. He had no further involvement in its operations.
After various mergers and ownership changes, Intel acquired McAfee in August 2010. In January 2014, Intel announced that McAfee-related products would be marketed as Intel Security. McAfee expressed his pleasure at the name change, saying, "I am now everlastingly grateful to Intel for freeing me from this terrible association with the worst software on the planet." The business was soon de-merged from Intel, once more under the McAfee name.
PowWow, QuoromEx, MGT and more
McAfee founded the company Tribal Voice in 1994, which developed one of the first instant messaging programs, PowWow.
In 2000, he invested in and joined the board of directors of Zone Labs, makers of firewall software, prior to its acquisition by Check Point Software in 2003. In the 2000s McAfee invested in and advertised ultra-light flights, which he marketed as aerotrekking.
In 2000 he bought a large property in Colorado and opened a yoga and meditation retreat there. In the following year he authored four books on yoga and meditation.
In August 2009 The New York Times reported that McAfee's personal fortune had declined to $4 million from a peak of $100 million due to the effect of the financial crisis of 2007–2008 on his investments.
McAfee relocated to Belize in 2009, buying a beachfront property on the island of Ambergris Caye and later also some property near the mainland village of Carmelita, where he surrounded himself with a large group of armed security guards.
In 2009, McAfee was interviewed in Belize for the CNBC special The Bubble Decade, in which it was reported that he had invested in and/or built many mansions in the USA that went unsold when the 2007 global recession hit. The report also discussed his quest to raise plants for possible medicinal uses on his land in Belize.
In February 2010, McAfee and biologist Allison Adonizio started the company QuorumEx, headquartered in Belize, which aimed to produce herbal antibiotics that disrupt quorum sensing in bacteria.
In June 2013, McAfee uploaded a parody video titled How to Uninstall McAfee Antivirus onto his YouTube channel. In it, he critiques the antivirus software while snorting white powder and being stripped by scantily clad women. It received ten million views. He told Reuters the video was meant to ridicule the media's negative coverage of him. A spokesman for McAfee Inc. called the video's statements "ludicrous".
Also in 2013, McAfee founded Future Tense Central, which aimed to produce a secure computer network device called the D-Central. By 2016, it was also an incubator.
In February 2014, McAfee announced Cognizant, an application for smartphones which displays information about the permissions of other installed applications. In April 2014, it was renamed DCentral 1, and an Android version was released for free on Google Play.
At the DEF CON conference in Las Vegas in August 2014, McAfee warned people not to use smartphones, suggesting apps are used to spy on clueless consumers who do not read privacy user agreements. In January 2016, he became the chief evangelist for security startup Everykey.
In February 2016, McAfee publicly volunteered to decrypt the iPhone used by Rizwan Farook and Tashfeen Malik in San Bernardino, avoiding the need for Apple to build a backdoor. He later admitted that his claims regarding the ease of cracking the phone were a publicity stunt, while still asserting its possibility.
In May 2016, McAfee was appointed chairman and CEO of MGT Capital Investments, a technology holding company. It initially said it would rename itself John McAfee Global Technologies, although this plan was abandoned due to a dispute with Intel over rights to the "McAfee" name. He changed MGT's focus from social gaming to cybersecurity, saying "anti-virus software is dead, it no longer works", and that "the new paradigm has to stop the hacker getting in" before they can do damage. The first product for this purpose was Sentinel.
Soon after joining MGT, McAfee said he and his team had exploited a flaw in the Android operating system that allowed him to read encrypted messages from WhatsApp. Gizmodo investigated his claim, and reported that he had sent reporters malware-infected phones to make this hack work. He replied: "Of course the phones had malware on them. How that malware got there is the story, which we will release after speaking with Google. It involves a serious flaw in the Android architecture."
McAfee moved MGT into the mining of bitcoin and other cryptocurrencies, both to make money for the company, and to increase MGT's expertise in dealing with blockchains, which he thought was important for cybersecurity.
In August 2017, McAfee stepped down as CEO, instead serving as MGT's "chief cybersecurity visionary." In January 2018, he left the company altogether. Both sides said the split was amicable; he said he wanted to spend all of his time on cryptocurrencies, while the company told of pressure from potential investors to disassociate itself from him.
On 13 August 2018, McAfee took a position of CEO with Luxcore, a cryptocurrency company focused on enterprise solutions.
Politics
Positions
McAfee was a libertarian, advocating the decriminalization of cannabis, an end to the war on drugs, non-interventionism in foreign policy, a free market economy which does not redistribute wealth, and upholding free trade. He supported abolishing the Transportation Security Administration.
McAfee advocated increased cyber awareness and more action against the threat of cyberwarfare. He pushed religious liberty, saying that business owners should be able to deny service in circumstances that contradict their religious beliefs, adding: "No one is forcing you to buy anything or to choose one person over another. So why should I be forced to do anything if I am not harming you? It's my choice to sell, your choice to buy."
McAfee contended that taxes were illegal, and claimed in 2019 that he had not filed a tax return since 2010. He referred to himself as "a prime target" of the Internal Revenue Service.
In July 2017, McAfee predicted on Twitter that the price of a bitcoin would jump to $500,000 within three years, adding: "If not, I will eat my own dick on national television." In July 2019, he predicted a price of $1 million by the end of 2020. In January 2020, he tweeted that his predictions were "a ruse to onboard new users," and that bitcoin had limited potential because it is "an ancient technology."
2016 presidential campaign
On 8 September 2015, McAfee announced a bid for president of the United States in the 2016 presidential election, as the candidate of a newly formed political party called the Cyber Party. On 24 December 2015, he re-announced his candidacy bid saying that he would instead seek the presidential nomination of the Libertarian Party. On the campaign trail, he consistently polled alongside the party's other top candidates, Gary Johnson and Austin Petersen. The three partook in the Libertarian Party's first nationally televised presidential debate on 29 March 2016. His running mate was photographer, commercial real estate broker and Libertarian activist Judd Weiss.
McAfee came in second in the primaries and third at the 2016 Libertarian National Convention.
Notable endorsements
Adam Kokesh, talk show host and activist
John Moore, Nevada assemblyman
L. Neil Smith, science fiction author and activist
2020 presidential campaign
Contrary to his assertion at the 2016 convention, McAfee tweeted on 3 June 2018 that he would run for president again in 2020, either with the Libertarian Party or a separate party that he would create. He later chose to run as a Libertarian. He mainly campaigned for wider cryptocurrency use.
On 22 January 2019, McAfee tweeted that he would continue his campaign "in exile," following reports that he, his wife, and four campaign staff were indicted for tax-related felonies by the IRS. He said he was in "international waters," and had previously tweeted that he was going to Venezuela. The IRS has not commented on the alleged indictments. He defended Marxist revolutionary Che Guevara on Twitter, putting himself at odds with Libertarian National Committee chairman Nicholas Sarwark, who wrote, "I hear very little buzz about McAfee this time around ... making a defense of Che Guevara from Cuba may ingratiate him with the Cuban government, but it didn't resonate well with Libertarians."
In a tweet on 4 March 2020, McAfee simultaneously suspended his 2020 presidential campaign, endorsed Vermin Supreme, and announced his campaign for the Libertarian Party vice presidential nomination. The next day, he returned to the presidential field, reversing the suspension of his bid, as "No one in the Libertarian Party Would consider me For Vice President." The next month, he endorsed Adam Kokesh and became Kokesh's vice-presidential candidate, while still seeking the presidency for himself. At the 2020 Libertarian National Convention, McAfee failed to qualify for the vice-presidential nomination.
Legal issues
McAfee was named a defendant in a 2008 civil court case related to his Aerotrekking light-sport aircraft venture and the death of nephew Joel Bitow and a passenger.
On 30 April 2012, McAfee's property in Orange Walk Town, Belize, was raided by the Gang Suppression Unit of the Belize Police Department. A GSU press release said he was arrested for unlicensed drug manufacturing and possession of an unlicensed weapon. He was released without charge. In December 2012, McAfee told a Wired reporter that from 2010 to 2011 he had made several posts to the drug discussion forum Bluelight discussing his use and manufacturing of the stimulant drug MDPV under the alias 'Stuffmonger'. As of March 2024, the Stuffmonger account had made 220 posts on the site in 2010 and early 2011.
In 2012, Belize police spokesman Raphael Martinez confirmed that McAfee was neither convicted nor charged, only suspected.
In January 2014, while in Canada, he said that when the Belizean government raided his property, it seized his assets, and that his house later burned down under suspicious circumstances.
On 2 August 2015, McAfee was arrested in Henderson County, Tennessee, on one count of driving under the influence and one count of possession of a firearm while intoxicated.
In July 2019, McAfee and members of his entourage were arrested while his yacht was docked at Puerto Plata, Dominican Republic, on suspicion of carrying high-caliber weapons and ammunition. They were held for four days and released. Weapons were seized, according to the Public Ministry.
On 11 August 2020, McAfee falsely stated that he was arrested in Norway during the COVID-19 pandemic after refusing to replace a lace thong with a more effective face mask. He later tweeted a picture of himself with a bruised eye, claiming it occurred during this arrest. A photo of the alleged arrest shows an officer with the German word for "police" on his uniform, ostensibly invalidating McAfee's claim of having been arrested in Norway. The Augsburg police later said he tried to enter Germany on that day, but was not arrested.
Death of Gregory Faull
On 12 November 2012, Belize police began to search for McAfee as a person of interest in connection to the homicide investigation of American immigrant Gregory Viant Faull, who was found dead of a gunshot wound the day before, at his home on the island of Ambergris Caye, the largest island in Belize. Faull was a neighbor of McAfee's. In a contemporary interview with Wired, McAfee said he had been afraid police would kill him and refused their routine questions and evaded them. He buried himself in sand for several hours with a cardboard box over his head. Belize's prime minister, Dean Barrow, called him "extremely paranoid, even bonkers". He fled Belize rather than cooperate.
In December 2012, the magazine Vice accidentally gave away McAfee's location at a Guatemalan resort, when a photo taken by one of its journalists accompanying him was posted with the EXIF geolocation metadata still attached.
While in Guatemala, McAfee asked Chad Essley, an American cartoonist and animator, to set up a blog so he could write about his experience while on the run. He then appeared publicly in Guatemala City, where he unsuccessfully sought political asylum.
On 5 December 2012, he was arrested for illegally entering Guatemala. Shortly afterward, the board reviewing his asylum plea denied it and he was taken to a detention center to await deportation to Belize.
On 6 December 2012, Reuters and ABC News reported that McAfee had two minor heart attacks in the detention center and was hospitalized. His lawyer said he had no heart attacks, rather high blood pressure and anxiety attacks. McAfee later said he faked the heart attacks to buy time for his attorney to file a series of appeals that ultimately prevented his deportation to Belize, thus hastening that government's decision to send him back to the United States.
On 12 December 2012, McAfee was released and deported to the United States.
On 14 November 2018, the Circuit Court in Orlando, Florida, refused to dismiss a wrongful death lawsuit against him for Faull's death. McAfee did not appear in court, lost the case by default and was ordered to pay $25 million to Faull's estate.
U.S. tax evasion charges and planned extradition
In January 2019, McAfee announced that he was on the run from U.S. authorities, and living internationally on a boat following the convening of a grand jury to indict him, his wife, and four of his 2020 Libertarian Party presidential primaries staff on tax evasion charges. At the time, the Internal Revenue Service had not independently confirmed the existence of any such indictment.
On 5 October 2020, McAfee was arrested in Spain at the request of the United States Department of Justice for tax evasion. The June indictment, which was unsealed upon his arrest, alleged he earned millions of dollars from 2014 to 2018, and failed to file income tax returns.
On 6 October, the U.S. Securities and Exchange Commission (SEC) filed a complaint further alleging McAfee and his bodyguard promoted certain initial coin offerings (ICOs) in a fraudulent cryptocurrency pump and dump scheme. It claims he presented himself as an impartial investor when he promoted the ICOs, despite allegedly getting paid $23 million in digital assets in return.
On 5 March 2021, the U.S. Attorney's Office for the
Southern District of New York formally indicted him and an executive adviser on these charges.
McAfee was jailed in Spain, pending extradition to the United States.
On 23 June 2021, the Spanish National Court authorized his extradition to face charges in Tennessee; McAfee is suspected to have committed suicide several hours after the authorization, though the official ruling has come under suspicion by the public as McAfee made his disintention to commit suicide clear by his tweet from 2019. The tweet, posted in November 2019, said: "Getting subtle messages from U.S. officials saying, in effect: 'We're coming for you McAfee! We're going to kill yourself'. I got a tattoo today just in case. If I suicide myself, I didn't. I was whackd. Check my right arm." It included a photo of a tattoo that said "$WHACKD." The New York extradition case was still pending in a lower Spanish court.
Personal life
McAfee married three times. He met his first wife, Fran, circa 1968 while he was working towards a doctorate at Northeast Louisiana State College and she was an 18-year-old undergraduate student. Their affair led to his expulsion from the college. He married his second wife, Judy, a former flight attendant at American Airlines, circa 1987; they divorced in 2002.
The night after McAfee arrived in the United States after being deported from Guatemala in December 2012, he was solicited by and slept with Janice Dyson, then a prostitute 30 years his junior in South Beach, Miami Beach, Florida. They began a relationship and married in 2013. She claims that he saved her from human traffickers. The couple moved to Portland, Oregon in 2013.
In a 2012 article in Mensa Bulletin, the magazine of the American Mensa, McAfee said developing the first commercial antivirus program had made him "the most popular hacking target" and "[h]ackers see hacking me as a badge of honor." For his own cybersecurity, he said he had other people buy his computer equipment for him, used pseudonyms for setting up computers and logins, and changed his IP address several times a day. When asked on another occasion if he personally used McAfee's antivirus software, he replied: "I take it off [...] it's too annoying."
According to a 2016 article, McAfee had been using the then legal drug alpha-PHP which he imported from China and which may have caused his paranoia. McAfee reportedly previously used the stimulant drug MDPV beginning in 2010, and was a member of the online drug discussion forum Bluelight.
In 2015, he resided in Lexington, Tennessee.
In December 2018, he tweeted that he had "47 genetic children." His third wife described him in a Father's Day message as "father of many, loved by few."
Death
On 23 June 2021, McAfee was found dead in his prison cell, hours after the Spanish National Court ordered his extradition to the United States on criminal charges filed in Tennessee by the United States Department of Justice Tax Division. The Catalan Justice Department said "everything indicates" he killed himself by hanging. An official autopsy confirmed his suicide. A Spanish court also ruled McAfee died by suicide.
McAfee's death ignited speculation and conspiracy theories about the possibility that he was murdered. Such speculation was particularly fueled by a 2019 post McAfee made on Twitter that read, in part, "If I suicide myself, I didn't. I was whackd ." McAfee's death drew comparisons to the circumstances of the death of American financier Jeffrey Epstein, who was found dead in August 2019 while awaiting trial on sex trafficking charges. Several times, McAfee claimed if he were ever found dead by hanging, it would mean he was murdered. The day after his death, his lawyer told reporters that while he regularly maintained contact with McAfee in prison, there were no signs of suicidal intent. McAfee's widow reaffirmed this position in her first public remarks since her husband's death, and also called for a "thorough" investigation.
On 14 December 2023, the morgue delivered McAfee's body to his family to be taken to the United States for his funeral. Until then, it had been kept in a refrigerator at the Justice City of Barcelona.
In the media
Gringo: The Dangerous Life of John McAfee is a Showtime Networks documentary about the portion of McAfee's life spent in Belize. It began airing in September 2016. It covers allegations of him drugging and sexually assaulting his business partner from QuorumEx, Allison Adonizio, and ordering the murders of Belizean David Middleton and American expat Gregory Faull. In an interview with Bloomberg's Pimm Fox and Kathleen Hayes on 8 September 2016, McAfee said these incidents were fabricated, and "Belize is a third-world banana republic and you can go down there and make any story you want if you pay your interviewees, which Showtime did."
Glenn Ficarra and John Requa stated in 2017 they would direct a film about McAfee titled King of the Jungle, written by Scott Alexander and Larry Karaszewski. At various points, Johnny Depp, Michael Keaton, and Seth Rogen were reported to have taken roles and later to have left the project. Zac Efron was reported to star as journalist Ari Furman.
McAfee and his wife were interviewed on ABC News's 20/20 regarding Faull's murder.
The 2022 documentary film Running With the Devil: The Wild World of John McAfee includes footage from an unreleased documentary by Vice, and interviews by Rocco Castoro, Alex Cody Foster, and Robert King.
Books
Computer Viruses, Worms, Data Diddlers, Killer Programs, and Other Threats to Your System. What They Are, How They Work, and How to Defend Your PC, Mac, or Mainframe, (with Colin Haynes) St. Martin's Press, 1989
The Secret of the Yamas: Spiritual Guide to Yoga, McAfee Pub, 2001
The Fabric of Self: Meditations on Vanity and Love, Woodland Publications, 2001
Into the Heart of Truth, Woodland Publications, 2001
Beyond the Siddhis. Supernatural Powers and the Sutras of Patanjali, Woodland Publications, 2001
References
Further reading
External links
Appearances on C-SPAN
John McAfee's website
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602,401 | https://en.wikipedia.org/wiki/Facial%20recognition%20system | A facial recognition system is a technology potentially capable of matching a human face from a digital image or a video frame against a database of faces. Such a system is typically employed to authenticate users through ID verification services, and works by pinpointing and measuring facial features from a given image.
Development began on similar systems in the 1960s, beginning as a form of computer application. Since their inception, facial recognition systems have seen wider uses in recent times on smartphones and in other forms of technology, such as robotics. Because computerized facial recognition involves the measurement of a human's physiological characteristics, facial recognition systems are categorized as biometrics. Although the accuracy of facial recognition systems as a biometric technology is lower than iris recognition, fingerprint image acquisition, palm recognition or voice recognition, it is widely adopted due to its contactless process. Facial recognition systems have been deployed in advanced human–computer interaction, video surveillance, law enforcement, passenger screening, decisions on employment and housing and automatic indexing of images.
Facial recognition systems are employed throughout the world today by governments and private companies. Their effectiveness varies, and some systems have previously been scrapped because of their ineffectiveness. The use of facial recognition systems has also raised controversy, with claims that the systems violate citizens' privacy, commonly make incorrect identifications, encourage gender norms and racial profiling, and do not protect important biometric data. The appearance of synthetic media such as deepfakes has also raised concerns about its security. These claims have led to the ban of facial recognition systems in several cities in the United States. Growing societal concerns led social networking company Meta Platforms to shut down its Facebook facial recognition system in 2021, deleting the face scan data of more than one billion users. The change represented one of the largest shifts in facial recognition usage in the technology's history. IBM also stopped offering facial recognition technology due to similar concerns.
History of facial recognition technology
Automated facial recognition was pioneered in the 1960s by Woody Bledsoe, Helen Chan Wolf, and Charles Bisson, whose work focused on teaching computers to recognize human faces. Their early facial recognition project was dubbed "man-machine" because a human first needed to establish the coordinates of facial features in a photograph before they could be used by a computer for recognition. Using a graphics tablet, a human would pinpoint facial features coordinates, such as the pupil centers, the inside and outside corners of eyes, and the widows peak in the hairline. The coordinates were used to calculate 20 individual distances, including the width of the mouth and of the eyes. A human could process about 40 pictures an hour, building a database of these computed distances. A computer would then automatically compare the distances for each photograph, calculate the difference between the distances, and return the closed records as a possible match.
In 1970, Takeo Kanade publicly demonstrated a face-matching system that located anatomical features such as the chin and calculated the distance ratio between facial features without human intervention. Later tests revealed that the system could not always reliably identify facial features. Nonetheless, interest in the subject grew and in 1977 Kanade published the first detailed book on facial recognition technology.
In 1993, the Defense Advanced Research Project Agency (DARPA) and the Army Research Laboratory (ARL) established the face recognition technology program FERET to develop "automatic face recognition capabilities" that could be employed in a productive real life environment "to assist security, intelligence, and law enforcement personnel in the performance of their duties." Face recognition systems that had been trialled in research labs were evaluated. The FERET tests found that while the performance of existing automated facial recognition systems varied, a handful of existing methods could viably be used to recognize faces in still images taken in a controlled environment. The FERET tests spawned three US companies that sold automated facial recognition systems. Vision Corporation and Miros Inc were founded in 1994, by researchers who used the results of the FERET tests as a selling point. Viisage Technology was established by a identification card defense contractor in 1996 to commercially exploit the rights to the facial recognition algorithm developed by Alex Pentland at MIT.
Following the 1993 FERET face-recognition vendor test, the Department of Motor Vehicles (DMV) offices in West Virginia and New Mexico became the first DMV offices to use automated facial recognition systems to prevent people from obtaining multiple driving licenses using different names. Driver's licenses in the United States were at that point a commonly accepted form of photo identification. DMV offices across the United States were undergoing a technological upgrade and were in the process of establishing databases of digital ID photographs. This enabled DMV offices to deploy the facial recognition systems on the market to search photographs for new driving licenses against the existing DMV database. DMV offices became one of the first major markets for automated facial recognition technology and introduced US citizens to facial recognition as a standard method of identification. The increase of the US prison population in the 1990s prompted U.S. states to established connected and automated identification systems that incorporated digital biometric databases, in some instances this included facial recognition. In 1999, Minnesota incorporated the facial recognition system FaceIT by Visionics into a mug shot booking system that allowed police, judges and court officers to track criminals across the state.
Until the 1990s, facial recognition systems were developed primarily by using photographic portraits of human faces. Research on face recognition to reliably locate a face in an image that contains other objects gained traction in the early 1990s with the principal component analysis (PCA). The PCA method of face detection is also known as Eigenface and was developed by Matthew Turk and Alex Pentland. Turk and Pentland combined the conceptual approach of the Karhunen–Loève theorem and factor analysis, to develop a linear model. Eigenfaces are determined based on global and orthogonal features in human faces. A human face is calculated as a weighted combination of a number of Eigenfaces. Because few Eigenfaces were used to encode human faces of a given population, Turk and Pentland's PCA face detection method greatly reduced the amount of data that had to be processed to detect a face. Pentland in 1994 defined Eigenface features, including eigen eyes, eigen mouths and eigen noses, to advance the use of PCA in facial recognition. In 1997, the PCA Eigenface method of face recognition was improved upon using linear discriminant analysis (LDA) to produce Fisherfaces. LDA Fisherfaces became dominantly used in PCA feature based face recognition. While Eigenfaces were also used for face reconstruction. In these approaches no global structure of the face is calculated which links the facial features or parts.
Purely feature based approaches to facial recognition were overtaken in the late 1990s by the Bochum system, which used Gabor filter to record the face features and computed a grid of the face structure to link the features. Christoph von der Malsburg and his research team at the University of Bochum developed Elastic Bunch Graph Matching in the mid-1990s to extract a face out of an image using skin segmentation. By 1997, the face detection method developed by Malsburg outperformed most other facial detection systems on the market. The so-called "Bochum system" of face detection was sold commercially on the market as ZN-Face to operators of airports and other busy locations. The software was "robust enough to make identifications from less-than-perfect face views. It can also often see through such impediments to identification as mustaches, beards, changed hairstyles and glasses—even sunglasses".
Real-time face detection in video footage became possible in 2001 with the Viola–Jones object detection framework for faces. Paul Viola and Michael Jones combined their face detection method with the Haar-like feature approach to object recognition in digital images to launch AdaBoost, the first real-time frontal-view face detector. By 2015, the Viola–Jones algorithm had been implemented using small low power detectors on handheld devices and embedded systems. Therefore, the Viola–Jones algorithm has not only broadened the practical application of face recognition systems but has also been used to support new features in user interfaces and teleconferencing.
Ukraine is using the US-based Clearview AI facial recognition software to identify dead Russian soldiers. Ukraine has conducted 8,600 searches and identified the families of 582 deceased Russian soldiers. The IT volunteer section of the Ukrainian army using the software is subsequently contacting the families of the deceased soldiers to raise awareness of Russian activities in Ukraine. The main goal is to destabilise the Russian government. It can be seen as a form of psychological warfare. About 340 Ukrainian government officials in five government ministries are using the technology. It is used to catch spies that might try to enter Ukraine.
Clearview AI's facial recognition database is only available to government agencies who may only use the technology to assist in the course of law enforcement investigations or in connection with national security.
The software was donated to Ukraine by Clearview AI. Russia is thought to be using it to find anti-war activists. Clearview AI was originally designed for US law enforcement. Using it in war raises new ethical concerns. One London based surveillance expert, Stephen Hare, is concerned it might make the Ukrainians appear inhuman: "Is it actually working? Or is it making [Russians] say: 'Look at these lawless, cruel Ukrainians, doing this to our boys'?"
Techniques for face recognition
While humans can recognize faces without much effort, facial recognition is a challenging pattern recognition problem in computing. Facial recognition systems attempt to identify a human face, which is three-dimensional and changes in appearance with lighting and facial expression, based on its two-dimensional image. To accomplish this computational task, facial recognition systems perform four steps. First face detection is used to segment the face from the image background. In the second step the segmented face image is aligned to account for face pose, image size and photographic properties, such as illumination and grayscale. The purpose of the alignment process is to enable the accurate localization of facial features in the third step, the facial feature extraction. Features such as eyes, nose and mouth are pinpointed and measured in the image to represent the face. The so established feature vector of the face is then, in the fourth step, matched against a database of faces.
Traditional
Some face recognition algorithms identify facial features by extracting landmarks, or features, from an image of the subject's face. For example, an algorithm may analyze the relative position, size, and/or shape of the eyes, nose, cheekbones, and jaw. These features are then used to search for other images with matching features.
Other algorithms normalize a gallery of face images and then compress the face data, only saving the data in the image that is useful for face recognition. A probe image is then compared with the face data. One of the earliest successful systems is based on template matching techniques applied to a set of salient facial features, providing a sort of compressed face representation.
Recognition algorithms can be divided into two main approaches: geometric, which looks at distinguishing features, or photo-metric, which is a statistical approach that distills an image into values and compares the values with templates to eliminate variances. Some classify these algorithms into two broad categories: holistic and feature-based models. The former attempts to recognize the face in its entirety while the feature-based subdivide into components such as according to features and analyze each as well as its spatial location with respect to other features.
Popular recognition algorithms include principal component analysis using eigenfaces, linear discriminant analysis, elastic bunch graph matching using the Fisherface algorithm, the hidden Markov model, the multilinear subspace learning using tensor representation, and the neuronal motivated dynamic link matching. Modern facial recognition systems make increasing use of machine learning techniques such as deep learning.
Human identification at a distance (HID)
To enable human identification at a distance (HID) low-resolution images of faces are enhanced using face hallucination. In CCTV imagery faces are often very small. But because facial recognition algorithms that identify and plot facial features require high resolution images, resolution enhancement techniques have been developed to enable facial recognition systems to work with imagery that has been captured in environments with a high signal-to-noise ratio. Face hallucination algorithms that are applied to images prior to those images being submitted to the facial recognition system use example-based machine learning with pixel substitution or nearest neighbour distribution indexes that may also incorporate demographic and age related facial characteristics. Use of face hallucination techniques improves the performance of high resolution facial recognition algorithms and may be used to overcome the inherent limitations of super-resolution algorithms. Face hallucination techniques are also used to pre-treat imagery where faces are disguised. Here the disguise, such as sunglasses, is removed and the face hallucination algorithm is applied to the image. Such face hallucination algorithms need to be trained on similar face images with and without disguise. To fill in the area uncovered by removing the disguise, face hallucination algorithms need to correctly map the entire state of the face, which may be not possible due to the momentary facial expression captured in the low resolution image.
3-dimensional recognition
Three-dimensional face recognition technique uses 3D sensors to capture information about the shape of a face. This information is then used to identify distinctive features on the surface of a face, such as the contour of the eye sockets, nose, and chin.
One advantage of 3D face recognition is that it is not affected by changes in lighting like other techniques. It can also identify a face from a range of viewing angles, including a profile view. Three-dimensional data points from a face vastly improve the precision of face recognition. 3D-dimensional face recognition research is enabled by the development of sophisticated sensors that project structured light onto the face. 3D matching technique are sensitive to expressions, therefore researchers at Technion applied tools from metric geometry to treat expressions as isometries. A new method of capturing 3D images of faces uses three tracking cameras that point at different angles; one camera will be pointing at the front of the subject, second one to the side, and third one at an angle. All these cameras will work together so it can track a subject's face in real-time and be able to face detect and recognize.
Thermal cameras
A different form of taking input data for face recognition is by using thermal cameras, by this procedure the cameras will only detect the shape of the head and it will ignore the subject accessories such as glasses, hats, or makeup. Unlike conventional cameras, thermal cameras can capture facial imagery even in low-light and nighttime conditions without using a flash and exposing the position of the camera. However, the databases for face recognition are limited. Efforts to build databases of thermal face images date back to 2004. By 2016, several databases existed, including the IIITD-PSE and the Notre Dame thermal face database. Current thermal face recognition systems are not able to reliably detect a face in a thermal image that has been taken of an outdoor environment.
In 2018, researchers from the U.S. Army Research Laboratory (ARL) developed a technique that would allow them to match facial imagery obtained using a thermal camera with those in databases that were captured using a conventional camera. Known as a cross-spectrum synthesis method due to how it bridges facial recognition from two different imaging modalities, this method synthesize a single image by analyzing multiple facial regions and details. It consists of a non-linear regression model that maps a specific thermal image into a corresponding visible facial image and an optimization issue that projects the latent projection back into the image space. ARL scientists have noted that the approach works by combining global information (i.e. features across the entire face) with local information (i.e. features regarding the eyes, nose, and mouth). According to performance tests conducted at ARL, the multi-region cross-spectrum synthesis model demonstrated a performance improvement of about 30% over baseline methods and about 5% over state-of-the-art methods.
Application
Social media
Founded in 2013, Looksery went on to raise money for its face modification app on Kickstarter. After successful crowdfunding, Looksery launched in October 2014. The application allows video chat with others through a special filter for faces that modifies the look of users. Image augmenting applications already on the market, such as Facetune and Perfect365, were limited to static images, whereas Looksery allowed augmented reality to live videos. In late 2015 SnapChat purchased Looksery, which would then become its landmark lenses function. Snapchat filter applications use face detection technology and on the basis of the facial features identified in an image a 3D mesh mask is layered over the face. A variety of technologies attempt to fool facial recognition software by the use of anti-facial recognition masks.
DeepFace is a deep learning facial recognition system created by a research group at Facebook. It identifies human faces in digital images. It employs a nine-layer neural net with over 120 million connection weights, and was trained on four million images uploaded by Facebook users. The system is said to be 97% accurate, compared to 85% for the FBI's Next Generation Identification system.
TikTok's algorithm has been regarded as especially effective, but many were left to wonder at the exact programming that caused the app to be so effective in guessing the user's desired content. In June 2020, TikTok released a statement regarding the "For You" page, and how they recommended videos to users, which did not include facial recognition. In February 2021, however, TikTok agreed to a $92 million settlement to a US lawsuit which alleged that the app had used facial recognition in both user videos and its algorithm to identify age, gender and ethnicity.
ID verification
The emerging use of facial recognition is in the use of ID verification services. Many companies and others are working in the market now to provide these services to banks, ICOs, and other e-businesses. Face recognition has been leveraged as a form of biometric authentication for various computing platforms and devices; Android 4.0 "Ice Cream Sandwich" added facial recognition using a smartphone's front camera as a means of unlocking devices, while Microsoft introduced face recognition login to its Xbox 360 video game console through its Kinect accessory, as well as Windows 10 via its "Windows Hello" platform (which requires an infrared-illuminated camera). In 2017, Apple's iPhone X smartphone introduced facial recognition to the product line with its "Face ID" platform, which uses an infrared illumination system.
Face ID
Apple introduced Face ID on the flagship iPhone X as a biometric authentication successor to the Touch ID, a fingerprint based system. Face ID has a facial recognition sensor that consists of two parts: a "Romeo" module that projects more than 30,000 infrared dots onto the user's face, and a "Juliet" module that reads the pattern. The pattern is sent to a local "Secure Enclave" in the device's central processing unit (CPU) to confirm a match with the phone owner's face.
The facial pattern is not accessible by Apple. The system will not work with eyes closed, in an effort to prevent unauthorized access. The technology learns from changes in a user's appearance, and therefore works with hats, scarves, glasses, and many sunglasses, beard and makeup. It also works in the dark. This is done by using a "Flood Illuminator", which is a dedicated infrared flash that throws out invisible infrared light onto the user's face to properly read the 30,000 facial points.
Healthcare
Facial recognition algorithms can help in diagnosing some diseases using specific features on the nose, cheeks and other part of the human face. Relying on developed data sets, machine learning has been used to identify genetic abnormalities just based on facial dimensions. FRT has also been used to verify patients before surgery procedures.
In March, 2022 according to a publication by Forbes, FDNA, an AI development company claimed that in the space of 10 years, they have worked with geneticists to develop a database of about 5,000 diseases and 1500 of them can be detected with facial recognition algorithms.
Deployment of FRT for availing government services
India
In an interview, the National Health Authority chief Dr. R.S. Sharma said that facial recognition technology would be used in conjunction with Aadhaar to authenticate the identity of people seeking vaccines. Ten human rights and digital rights organizations and more than 150 individuals signed a statement by the Internet Freedom Foundation that raised alarm against the deployment of facial recognition technology in the central government's vaccination drive process. Implementation of an error-prone system without adequate legislation containing mandatory safeguards, would deprive citizens of essential services and linking this untested technology to the vaccination roll-out in India will only exclude persons from the vaccine delivery system.
In July, 2021, a press release by the Government of Meghalaya stated that facial recognition technology (FRT) would be used to verify the identity of pensioners to issue a Digital Life Certificate using "Pensioner's Life Certification Verification" mobile application. The notice, according to the press release, purports to offer pensioners "a secure, easy and hassle-free interface for verifying their liveness to the Pension Disbursing Authorities from the comfort of their homes using smart phones". Mr. Jade Jeremiah Lyngdoh, a law student, sent a legal notice to the relevant authorities highlighting that "The application has been rolled out without any anchoring legislation which governs the processing of personal data and thus, lacks lawfulness and the Government is not empowered to process data."
Deployment in security services
Commonwealth
The Australian Border Force and New Zealand Customs Service have set up an automated border processing system called SmartGate that uses face recognition, which compares the face of the traveller with the data in the e-passport microchip. All Canadian international airports use facial recognition as part of the Primary Inspection Kiosk program that compares a traveler face to their photo stored on the ePassport. This program first came to Vancouver International Airport in early 2017 and was rolled up to all remaining international airports in 2018–2019.
Police forces in the United Kingdom have been trialing live facial recognition technology at public events since 2015. In May 2017, a man was arrested using an automatic facial recognition (AFR) system mounted on a van operated by the South Wales Police. Ars Technica reported that "this appears to be the first time [AFR] has led to an arrest". However, a 2018 report by Big Brother Watch found that these systems were up to 98% inaccurate. The report also revealed that two UK police forces, South Wales Police and the Metropolitan Police, were using live facial recognition at public events and in public spaces.
In September 2019, South Wales Police use of facial recognition was ruled lawful. Live facial recognition has been trialled since 2016 in the streets of London and will be used on a regular basis from Metropolitan Police from beginning of 2020. In August 2020 the Court of Appeal ruled that the way the facial recognition system had been used by the South Wales Police in 2017 and 2018 violated human rights.
However, by 2024 the Metropolitan Police were using the technique with a database of 16,000 suspects, leading to over 360 arrests, including rapists and someone wanted for grievous bodily harm for 8 years. They claim a false positive rate of only 1 in 6,000. The photos of those not identified by the system are deleted immediately.
United States
The U.S. Department of State operates one of the largest face recognition systems in the world with a database of 117 million American adults, with photos typically drawn from driver's license photos. Although it is still far from completion, it is being put to use in certain cities to give clues as to who was in the photo. The FBI uses the photos as an investigative tool, not for positive identification. facial recognition was being used to identify people in photos taken by police in San Diego and Los Angeles (not on real-time video, and only against booking photos) and use was planned in West Virginia and Dallas.
In recent years Maryland has used face recognition by comparing people's faces to their driver's license photos. The system drew controversy when it was used in Baltimore to arrest unruly protesters after the death of Freddie Gray in police custody. Many other states are using or developing a similar system however some states have laws prohibiting its use.
The FBI has also instituted its Next Generation Identification program to include face recognition, as well as more traditional biometrics like fingerprints and iris scans, which can pull from both criminal and civil databases. The federal Government Accountability Office criticized the FBI for not addressing various concerns related to privacy and accuracy.
Starting in 2018, U.S. Customs and Border Protection deployed "biometric face scanners" at U.S. airports. Passengers taking outbound international flights can complete the check-in, security and the boarding process after getting facial images captured and verified by matching their ID photos stored on CBP's database. Images captured for travelers with U.S. citizenship will be deleted within up to 12-hours. The Transportation Security Administration (TSA) had expressed its intention to adopt a similar program for domestic air travel during the security check process in the future. The American Civil Liberties Union is one of the organizations against the program, concerning that the program will be used for surveillance purposes.
In 2019, researchers reported that Immigration and Customs Enforcement (ICE) uses facial recognition software against state driver's license databases, including for some states that provide licenses to undocumented immigrants.
In December 2022, 16 major domestic airports in the US started testing facial-recognition tech where kiosks with cameras are checking the photos on travelers' IDs to make sure that passengers are not impostors.
China
In 2006, the "Skynet" (天網）)Project was initiated by the Chinese government to implement CCTV surveillance nationwide and there have been 20 million cameras, many of which are capable of real-time facial recognition, deployed across the country for this project. Some official claim that the current Skynet system can scan the entire Chinese population in one second and the world population in two seconds.
In 2017, the Qingdao police was able to identify twenty-five wanted suspects using facial recognition equipment at the Qingdao International Beer Festival, one of which had been on the run for 10 years. The equipment works by recording a 15-second video clip and taking multiple snapshots of the subject. That data is compared and analyzed with images from the police department's database and within 20 minutes, the subject can be identified with a 98.1% accuracy.
In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas.
China has deployed facial recognition and artificial intelligence technology in Xinjiang. Reporters visiting the region found surveillance cameras installed every hundred meters or so in several cities, as well as facial recognition checkpoints at areas like gas stations, shopping centers, and mosque entrances. In May 2019, Human Rights Watch reported finding Face++ code in the Integrated Joint Operations Platform (IJOP), a police surveillance app used to collect data on, and track the Uighur community in Xinjiang. Human Rights Watch released a correction to its report in June 2019 stating that the Chinese company Megvii did not appear to have collaborated on IJOP, and that the Face++ code in the app was inoperable. In February 2020, following the Coronavirus outbreak, Megvii applied for a bank loan to optimize the body temperature screening system it had launched to help identify people with symptoms of a Coronavirus infection in crowds. In the loan application Megvii stated that it needed to improve the accuracy of identifying masked individuals.
Many public places in China are implemented with facial recognition equipment, including railway stations, airports, tourist attractions, expos, and office buildings. In October 2019, a professor at Zhejiang Sci-Tech University sued the Hangzhou Safari Park for abusing private biometric information of customers. The safari park uses facial recognition technology to verify the identities of its Year Card holders. An estimated 300 tourist sites in China have installed facial recognition systems and use them to admit visitors. This case is reported to be the first on the use of facial recognition systems in China. In August 2020, Radio Free Asia reported that in 2019 Geng Guanjun, a citizen of Taiyuan City who had used the WeChat app by Tencent to forward a video to a friend in the United States was subsequently convicted on the charge of the crime "picking quarrels and provoking troubles". The Court documents showed that the Chinese police used a facial recognition system to identify Geng Guanjun as an "overseas democracy activist" and that China's network management and propaganda departments directly monitor WeChat users.
In 2019, Protestors in Hong Kong destroyed smart lampposts amid concerns they could contain cameras and facial recognition system used for surveillance by Chinese authorities. Human rights groups have criticized the Chinese government for using artificial intelligence facial recognition technology in its suppression against Uyghurs, Christians and Falun Gong practitioners.
India
Even though facial recognition technology (FRT) is not fully accurate, it is being increasingly deployed for identification purposes by the police in India. FRT systems generate a probability match score, or a confidence score between the suspect who is to be identified and the database of identified criminals that is available with the police. The National Automated Facial Recognition System (AFRS) is already being developed by the National Crime Records Bureau (NCRB), a body constituted under the Ministry of Home Affairs. The project seeks to develop and deploy a national database of photographs which would comport with a facial recognition technology system by the central and state security agencies. The Internet Freedom Foundation has flagged concerns regarding the project. The NGO has highlighted that the accuracy of FRT systems are "routinely exaggerated and the real numbers leave much to be desired. The implementation of such faulty FRT systems would lead to high rates of false positives and false negatives in this recognition process."
Under the Supreme Court of India's decision in Justice K.S. Puttaswamy vs Union of India (22017 10 SCC 1), any justifiable intrusion by the State into people's right to privacy, which is protected as a fundamental right under Article 21 of the Constitution, must confirm to certain thresholds, namely: legality, necessity, proportionality and procedural safeguards. As per the Internet Freedom Foundation, the National Automated Facial Recognition System (AFRS) proposal fails to meet any of these thresholds, citing "absence of legality," "manifest arbitrariness," and "absence of safeguards and accountability."
While the national level AFRS project is still in the works, police departments in various states in India are already deploying facial recognition technology systems, such as: TSCOP + CCTNS in Telangana, Punjab Artificial Intelligence System (PAIS) in Punjab, Trinetra in Uttar Pradesh, Police Artificial Intelligence System in Uttarakhand, AFRS in Delhi, Automated Multimodal Biometric Identification System (AMBIS) in Maharashtra, FaceTagr in Tamil Nadu. The Crime and Criminal Tracking Network and Systems (CCTNS), which is a Mission Mode Project under the National e-Governance Plan (NeGP), is viewed as a system which would connect police stations across India, and help them "talk" to each other. The project's objective is to digitize all FIR-related information, including FIRs registered, as well as cases investigated, charge sheets filed, and suspects and wanted persons in all police stations. This shall constitute a national database of crime and criminals in India. CCTNS is being implemented without a data protection law in place. CCTNS is proposed to be integrated with the AFRS, a repository of all crime and criminal related facial data which can be deployed to purportedly identify or verify a person from a variety of inputs ranging from images to videos. This has raised privacy concerns from civil society organizations and privacy experts. Both the projects have been censured as instruments of "mass surveillance" at the hands of the state. In Rajasthan, 'RajCop,' a police app has been recently integrated with a facial recognition module which can match the face of a suspect against a database of known persons in real-time. Rajasthan police is in currently working to widen the ambit of this module by making it mandatory to upload photographs of all arrested persons in CCTNS database, which will "help develop a rich database of known offenders."
Helmets fixed with camera have been designed and being used by Rajasthan police in law and order situations to capture police action and activities of "the miscreants, which can later serve as evidence during the investigation of such cases." PAIS (Punjab Artificial Intelligence System), App employs deep learning, machine learning, and face recognition for the identification of criminals to assist police personnel. The state of Telangana has installed 8 lakh CCTV cameras, with its capital city Hyderabad slowly turning into a surveillance capital.
A false positive happens when facial recognition technology misidentifies a person to be someone they are not, that is, it yields an incorrect positive result. They often results in discrimination and strengthening of existing biases. For example, in 2018, Delhi Police reported that its FRT system had an accuracy rate of 2%, which sank to 1% in 2019. The FRT system even failed to distinguish accurately between different sexes.
The government of Delhi in collaboration with Indian Space Research Organisation (ISRO) is developing a new technology called Crime Mapping Analytics and Predictive System (CMAPS). The project aims to deploy space technology for "controlling crime and maintaining law and order." The system will be connected to a database containing data of criminals. The technology is envisaged to be deployed to collect real-time data at the crime scene.
In a reply dated November 25, 2020 to a Right to Information request filed by the Internet Freedom Foundation seeking information about the facial recognition system being used by the Delhi Police (with reference number DEPOL/R/E/20/07128), the Office of the Deputy Commissioner of Police cum Public Information Officer: Crime stated that they cannot provide the information under section 8(d) of the Right to Information Act, 2005.
A Right to Information (RTI) request dated July 30, 2020 was filed with the Office of the Commissioner, Kolkata Police, seeking information about the facial recognition technology that the department was using. The information sought was denied stating that the department was exempted from disclosure under section 24(4) of the RTI Act.
Latin America
In the 2000 Mexican presidential election, the Mexican government employed face recognition software to prevent voter fraud. Some individuals had been registering to vote under several different names, in an attempt to place multiple votes. By comparing new face images to those already in the voter database, authorities were able to reduce duplicate registrations.
In Colombia public transport busses are fitted with a facial recognition system by FaceFirst Inc to identify passengers that are sought by the National Police of Colombia. FaceFirst Inc also built the facial recognition system for Tocumen International Airport in Panama. The face recognition system is deployed to identify individuals among the travellers that are sought by the Panamanian National Police or Interpol. Tocumen International Airport operates an airport-wide surveillance system using hundreds of live face recognition cameras to identify wanted individuals passing through the airport. The face recognition system was initially installed as part of a US$11 million contract and included a computer cluster of sixty computers, a fiber-optic cable network for the airport buildings, as well as the installation of 150 surveillance cameras in the airport terminal and at about 30 airport gates.
At the 2014 FIFA World Cup in Brazil the Federal Police of Brazil used face recognition goggles. Face recognition systems "made in China" were also deployed at the 2016 Summer Olympics in Rio de Janeiro. Nuctech Company provided 145 inspection terminals for Maracanã Stadium and 55 terminals for the Deodoro Olympic Park.
European Union
Police forces in at least 21 countries of the European Union use, or plan to use, facial recognition systems, either for administrative or criminal purposes.
Greece
Greek police passed a contract with Intracom-Telecom for the provision of at least 1,000 devices equipped with live facial recognition system. The delivery is expected before the summer 2021. The total value of the contract is over 4 million euros, paid for in large part by the Internal Security Fund of the European Commission.
Italy
Italian police acquired a face recognition system in 2017, Sistema Automatico Riconoscimento Immagini (SARI). In November 2020, the Interior ministry announced plans to use it in real-time to identify people suspected of seeking asylum.
The Netherlands
The Netherlands has deployed facial recognition and artificial intelligence technology since 2016. The database of the Dutch police currently contains over 2.2 million pictures of 1.3 million Dutch citizens. This accounts for about 8% of the population. In The Netherlands, face recognition is not used by the police on municipal CCTV.
South Africa
In South Africa, in 2016, the city of Johannesburg announced it was rolling out smart CCTV cameras complete with automatic number plate recognition and facial recognition.
Deployment in retail stores
The US firm 3VR, now Identiv, is an example of a vendor which began offering facial recognition systems and services to retailers as early as 2007. In 2012, the company advertised benefits such as "dwell and queue line analytics to decrease customer wait times", "facial surveillance analytic[s] to facilitate personalized customer greetings by employees" and the ability to "[c]reate loyalty programs by combining Point of sale (POS) data with facial recognition".
United States
In 2018, the National Retail Federation Loss Prevention Research Council called facial recognition technology "a promising new tool" worth evaluating.
In July 2020, the Reuters news agency reported that during the 2010s the pharmacy chain Rite Aid had deployed facial recognition video surveillance systems and components from FaceFirst, DeepCam LLC, and other vendors at some retail locations in the United States. Cathy Langley, Rite Aid's vice president of asset protection, used the phrase "feature matching" to refer to the systems and said that usage of the systems resulted in less violence and organized crime in the company's stores, while former vice president of asset protection Bob Oberosler emphasized improved safety for staff and a reduced need for the involvement of law enforcement organizations. In a 2020 statement to Reuters in response to the reporting, Rite Aid said that it had ceased using the facial recognition software and switched off the cameras.
According to director Read Hayes of the National Retail Federation Loss Prevention Research Council, Rite Aid's surveillance program was either the largest or one of the largest programs in retail. The Home Depot, Menards, Walmart, and 7-Eleven are among other US retailers also engaged in large-scale pilot programs or deployments of facial recognition technology.
Of the Rite Aid stores examined by Reuters in 2020, those in communities where people of color made up the largest racial or ethnic group were three times as likely to have the technology installed, raising concerns related to the substantial history of racial segregation and racial profiling in the United States. Rite Aid said that the selection of locations was "data-driven", based on the theft histories of individual stores, local and national crime data, and site infrastructure.
Australia
In 2019, facial recognition to prevent theft was in use at Sydney's Star Casino and was also deployed at gaming venues in New Zealand.
In June 2022, consumer group CHOICE reported facial recognition was in use in Australia at Kmart, Bunnings, and The Good Guys. The Good Guys subsequently suspended the technology pending a legal challenge by CHOICE to the Office of the Australian Information Commissioner, while Bunnings kept the technology in use and Kmart maintained its trial of the technology.
Additional uses
At the American football championship game Super Bowl XXXV in January 2001, police in Tampa Bay, Florida used Viisage face recognition software to search for potential criminals and terrorists in attendance at the event. 19 people with minor criminal records were potentially identified.
Face recognition systems have also been used by photo management software to identify the subjects of photographs, enabling features such as searching images by person, as well as suggesting photos to be shared with a specific contact if their presence were detected in a photo. By 2008 facial recognition systems were typically used as access control in security systems.
The United States' popular music and country music celebrity Taylor Swift surreptitiously employed facial recognition technology at a concert in 2018. The camera was embedded in a kiosk near a ticket booth and scanned concert-goers as they entered the facility for known stalkers.
On August 18, 2019, The Times reported that the UAE-owned Manchester City hired a Texas-based firm, Blink Identity, to deploy facial recognition systems in a driver program. The club has planned a single super-fast lane for the supporters at the Etihad stadium. However, civil rights groups cautioned the club against the introduction of this technology, saying that it would risk "normalising a mass surveillance tool". The policy and campaigns officer at Liberty, Hannah Couchman said that Man City's move is alarming, since the fans will be obliged to share deeply sensitive personal information with a private company, where they could be tracked and monitored in their everyday lives.
In 2019, casinos in Australia and New Zealand rolled out facial recognition to prevent theft, and a representative of Sydney's Star Casino said they would also provide 'customer service' like welcoming a patron back to a bar.
In August 2020, amid the COVID-19 pandemic in the United States, American football stadiums of New York and Los Angeles announced the installation of facial recognition for upcoming matches. The purpose is to make the entry process as touchless as possible. Disney's Magic Kingdom, near Orlando, Florida, likewise announced a test of facial recognition technology to create a touchless experience during the pandemic; the test was originally slated to take place between March 23 and April 23, 2021, but the limited timeframe had been removed
Media companies have begun using face recognition technology to streamline their tracking, organizing, and archiving pictures and videos.
Advantages and disadvantages
Compared to other biometric systems
In 2006, the performance of the latest face recognition algorithms was evaluated in the Face Recognition Grand Challenge (FRGC). High-resolution face images, 3-D face scans, and iris images were used in the tests. The results indicated that the new algorithms are 10 times more accurate than the face recognition algorithms of 2002 and 100 times more accurate than those of 1995. Some of the algorithms were able to outperform human participants in recognizing faces and could uniquely identify identical twins.
One key advantage of a facial recognition system that it is able to perform mass identification as it does not require the cooperation of the test subject to work. Properly designed systems installed in airports, multiplexes, and other public places can identify individuals among the crowd, without passers-by even being aware of the system. However, as compared to other biometric techniques, face recognition may not be most reliable and efficient. Quality measures are very important in facial recognition systems as large degrees of variations are possible in face images. Factors such as illumination, expression, pose and noise during face capture can affect the performance of facial recognition systems. Among all biometric systems, facial recognition has the highest false acceptance and rejection rates, thus questions have been raised on the effectiveness of or bias of face recognition software in cases of railway and airport security, law enforcement and housing and employment decisions.
Weaknesses
Ralph Gross, a researcher at the Carnegie Mellon Robotics Institute in 2008, describes one obstacle related to the viewing angle of the face: "Face recognition has been getting pretty good at full frontal faces and 20 degrees off, but as soon as you go towards profile, there've been problems." Besides the pose variations, low-resolution face images are also very hard to recognize. This is one of the main obstacles of face recognition in surveillance systems. It has also been suggested that camera settings can favour sharper imagery of white skin than of other skin tones.
Face recognition is less effective if facial expressions vary. A big smile can render the system less effective. For instance: Canada, in 2009, allowed only neutral facial expressions in passport photos.
There is also inconstancy in the datasets used by researchers. Researchers may use anywhere from several subjects to scores of subjects and a few hundred images to thousands of images. Data sets may be diverse and inclusive or mainly contain images of white males. It is important for researchers to make available the datasets they used to each other, or have at least a standard or representative dataset.
Although high degrees of accuracy have been claimed for some facial recognition systems, these outcomes are not universal. The consistently worst accuracy rate is for those who are 18 to 30 years old, Black and female.
Racial bias and skin tone
Studies have shown that facial recognition algorithms tend to perform better on individuals with lighter skin tones compared to those with darker skin tones. This disparity arises primarily because training datasets often overrepresent lighter-skinned individuals, leading to higher error rates for darker-skinned people. For example, a 2018 study found that leading commercial gender classification models, which are facial recognition models, have an error rate up to 7 times higher for those with darker skin tones compared to those with lighter skin tones.
Common image compression methods, such as JPEG chroma subsampling, have been found to disproportionately degrade performance for darker-skinned individuals. These methods inadequately represent color information, which adversely affects the ability of algorithms to recognize darker-skinned individuals accurately.
Cross-race effect bias
Facial recognition systems often demonstrate lower accuracy when identifying individuals with non-Eurocentric facial features. Known as the Cross-race effect, this bias occurs when systems perform better on racial or ethnic groups that are overrepresented in their training data, resulting in reduced accuracy for underrepresented groups. The overrepresented group is generally the more populous group in the location that the model is being developed. For example, models developed in Asian cultures generally perform better on Asian facial features than Eurocentric facial features due to overrepresentation in the developers training dataset. The opposite is observed in models developed in Eurocentric cultures.
The cross-race effect is not exclusive to machines; humans also experience difficulty recognizing faces from racial or ethnic groups different from their own. This is an example of inherent human biases being perpetuated in training datasets.
Challenges for individuals with disabilities
Facial recognition technologies encounter significant challenges when identifying individuals with disabilities. For instance, systems have been shown to perform worse when recognizing individuals with Down syndrome, often leading to increased false match rates. This is due to distinct facial structures associated with the condition that are not adequately represented in training datasets.
More broadly, facial recognition systems tend to overlook diverse physical characteristics related to disabilities. The lack of representative data for individuals with varying disabilities further emphasizes the need for inclusive algorithmic designs to mitigate bias and improve accuracy.
Additionally, facial expression recognition technologies often fail to accurately interpret the emotional states of individuals with intellectual disabilities. This shortcoming can hinder effective communication and interaction, underscoring the necessity for systems trained on diverse datasets that include individuals with intellectual disabilities.
Furthermore, biases in facial recognition algorithms can lead to discriminatory outcomes for people with disabilities. For example, certain facial features or asymmetries may result in misidentification or exclusion, highlighting the importance of developing accessible and fair biometric systems.
Advancements in fairness and mitigation strategies
Efforts to address these biases include designing algorithms specifically for fairness. A notable study introduced a method to learn fair face representations by using a progressive cross-transformer model. This approach highlights the importance of balancing accuracy across demographic groups while avoiding performance drops in specific populations.
Additionally, targeted dataset collection has been shown to improve racial equity in facial recognition systems. By prioritizing diverse data inputs, researchers demonstrated measurable reductions in performance disparities between racial groups.
Ineffectiveness
Critics of the technology complain that the London Borough of Newham scheme has, never recognized a single criminal, despite several criminals in the system's database living in the Borough and the system has been running for several years. "Not once, as far as the police know, has Newham's automatic face recognition system spotted a live target." This information seems to conflict with claims that the system was credited with a 34% reduction in crime (hence why it was rolled out to Birmingham also).
An experiment in 2002 by the local police department in Tampa, Florida, had similarly disappointing results. A system at Boston's Logan Airport was shut down in 2003 after failing to make any matches during a two-year test period.
In 2014, Facebook stated that in a standardized two-option facial recognition test, its online system scored 97.25% accuracy, compared to the human benchmark of 97.5%.
Systems are often advertised as having accuracy near 100%; this is misleading as the outcomes are not universal The studies often use samples that are smaller and less diverse than would be necessary for large scale applications. Because facial recognition is not completely accurate, it creates a list of potential matches. A human operator must then look through these potential matches and studies show the operators pick the correct match out of the list only about half the time. This causes the issue of targeting the wrong suspect.
Controversies
Privacy violations
Civil rights organizations and privacy campaigners such as the Electronic Frontier Foundation, Big Brother Watch and the ACLU express concern that privacy is being compromised by the use of surveillance technologies. Face recognition can be used not just to identify an individual, but also to unearth other personal data associated with an individual – such as other photos featuring the individual, blog posts, social media profiles, Internet behavior, and travel patterns. Concerns have been raised over who would have access to the knowledge of one's whereabouts and people with them at any given time. Moreover, individuals have limited ability to avoid or thwart face recognition tracking unless they hide their faces. This fundamentally changes the dynamic of day-to-day privacy by enabling any marketer, government agency, or random stranger to secretly collect the identities and associated personal information of any individual captured by the face recognition system. Consumers may not understand or be aware of what their data is being used for, which denies them the ability to consent to how their personal information gets shared.
In July 2015, the United States Government Accountability Office conducted a Report to the Ranking Member, Subcommittee on Privacy, Technology and the Law, Committee on the Judiciary, U.S. Senate. The report discussed facial recognition technology's commercial uses, privacy issues, and the applicable federal law. It states that previously, issues concerning facial recognition technology were discussed and represent the need for updating the privacy laws of the United States so that federal law continually matches the impact of advanced technologies. The report noted that some industry, government, and private organizations were in the process of developing, or have developed, "voluntary privacy guidelines". These guidelines varied between the stakeholders, but their overall aim was to gain consent and inform citizens of the intended use of facial recognition technology. According to the report the voluntary privacy guidelines helped to counteract the privacy concerns that arise when citizens are unaware of how their personal data gets put to use.
In 2016, Russian company NtechLab caused a privacy scandal in the international media when it launched the FindFace face recognition system with the promise that Russian users could take photos of strangers in the street and link them to a social media profile on the social media platform Vkontakte (VK). In December 2017, Facebook rolled out a new feature that notifies a user when someone uploads a photo that includes what Facebook thinks is their face, even if they are not tagged. Facebook has attempted to frame the new functionality in a positive light, amidst prior backlashes. Facebook's head of privacy, Rob Sherman, addressed this new feature as one that gives people more control over their photos online. "We've thought about this as a really empowering feature," he says. "There may be photos that exist that you don't know about." Facebook's DeepFace has become the subject of several class action lawsuits under the Biometric Information Privacy Act, with claims alleging that Facebook is collecting and storing face recognition data of its users without obtaining informed consent, in direct violation of the 2008 Biometric Information Privacy Act (BIPA). The most recent case was dismissed in January 2016 because the court lacked jurisdiction. In the US, surveillance companies such as Clearview AI are relying on the First Amendment to the United States Constitution to data scrape user accounts on social media platforms for data that can be used in the development of facial recognition systems.
In 2019, the Financial Times first reported that facial recognition software was in use in the King's Cross area of London. The development around London's King's Cross mainline station includes shops, offices, Google's UK HQ and part of St Martin's College. According to the UK Information Commissioner's Office: "Scanning people's faces as they lawfully go about their daily lives, in order to identify them, is a potential threat to privacy that should concern us all." The UK Information Commissioner Elizabeth Denham launched an investigation into the use of the King's Cross facial recognition system, operated by the company Argent. In September 2019 it was announced by Argent that facial recognition software would no longer be used at King's Cross. Argent claimed that the software had been deployed between May 2016 and March 2018 on two cameras covering a pedestrian street running through the centre of the development. In October 2019, a report by the deputy London mayor Sophie Linden revealed that in a secret deal the Metropolitan Police had passed photos of seven people to Argent for use in their King's cross facial recognition system.
Automated Facial Recognition was trialled by the South Wales Police on multiple occasions between 2017 and 2019. The use of the technology was challenged in court by a private individual, Edward Bridges, with support from the charity Liberty (case known as R (Bridges) v Chief Constable South Wales Police). The case was heard in the Court of Appeal and a judgement was given in August 2020. The case argued that the use of Facial Recognition was a privacy violation on the basis that there was insufficient legal framework or proportionality in the use of Facial Recognition and that its use was in violation of the Data Protection Acts 1998 and 2018. The case was decided in favour of Bridges and did not award damages. The case was settled via a declaration of wrongdoing. In response to the case, the British Government has repeatedly attempted to pass a Bill regulating the use of Facial Recognition in public spaces. The proposed Bills have attempted to appoint a Commissioner with the ability to regulate Facial Recognition use by Government Services in a similar manner to the Commissioner for CCTV. Such a Bill has yet to come into force [correct ].
In January 2023, New York Attorney General Letitia James asked for more information on the use of facial recognition technology from Madison Square Garden Entertainment following reports that the firm used it to block lawyers involved in litigation against the company from entering Madison Square Garden. She noted such a move would could go against federal, state, and local human rights laws.
Imperfect technology in law enforcement
it is still contested as to whether or not facial recognition technology works less accurately on people of color. One study by Joy Buolamwini (MIT Media Lab) and Timnit Gebru (Microsoft Research) found that the error rate for gender recognition for women of color within three commercial facial recognition systems ranged from 23.8% to 36%, whereas for lighter-skinned men it was between 0.0 and 1.6%. Overall accuracy rates for identifying men (91.9%) were higher than for women (79.4%), and none of the systems accommodated a non-binary understanding of gender. It also showed that the datasets used to train commercial facial recognition models were unrepresentative of the broader population and skewed toward lighter-skinned males. However, another study showed that several commercial facial recognition software sold to law enforcement offices around the country had a lower false non-match rate for black people than for white people.
Experts fear that face recognition systems may actually be hurting citizens the police claims they are trying to protect. It is considered an imperfect biometric, and in a study conducted by Georgetown University researcher Clare Garvie, she concluded that "there's no consensus in the scientific community that it provides a positive identification of somebody." It is believed that with such large margins of error in this technology, both legal advocates and facial recognition software companies say that the technology should only supply a portion of the case – no evidence that can lead to an arrest of an individual. The lack of regulations holding facial recognition technology companies to requirements of racially biased testing can be a significant flaw in the adoption of use in law enforcement. CyberExtruder, a company that markets itself to law enforcement said that they had not performed testing or research on bias in their software. CyberExtruder did note that some skin colors are more difficult for the software to recognize with current limitations of the technology. "Just as individuals with very dark skin are hard to identify with high significance via facial recognition, individuals with very pale skin are the same," said Blake Senftner, a senior software engineer at CyberExtruder.
The United States' National Institute of Standards and Technology (NIST) carried out extensive testing of FRT system 1:1 verification and 1:many identification. It also tested for the differing accuracy of FRT across different demographic groups. The independent study concluded at present, no FRT system has 100% accuracy.
Data protection
In 2010, Peru passed the Law for Personal Data Protection, which defines biometric information that can be used to identify an individual as sensitive data. In 2012, Colombia passed a comprehensive Data Protection Law which defines biometric data as senstivite information. According to Article 9(1) of the EU's 2016 General Data Protection Regulation (GDPR) the processing of biometric data for the purpose of "uniquely identifying a natural person" is sensitive and the facial recognition data processed in this way becomes sensitive personal data. In response to the GDPR passing into the law of EU member states, EU based researchers voiced concern that if they were required under the GDPR to obtain individual's consent for the processing of their facial recognition data, a face database on the scale of MegaFace could never be established again. In September 2019 the Swedish Data Protection Authority (DPA) issued its first ever financial penalty for a violation of the EU's General Data Protection Regulation (GDPR) against a school that was using the technology to replace time-consuming roll calls during class. The DPA found that the school illegally obtained the biometric data of its students without completing an impact assessment. In addition the school did not make the DPA aware of the pilot scheme. A 200,000 SEK fine (€19,000/$21,000) was issued.
In the United States of America several U.S. states have passed laws to protect the privacy of biometric data. Examples include the Illinois Biometric Information Privacy Act (BIPA) and the California Consumer Privacy Act (CCPA). In March 2020 California residents filed a class action against Clearview AI, alleging that the company had illegally collected biometric data online and with the help of face recognition technology built up a database of biometric data which was sold to companies and police forces. At the time Clearview AI already faced two lawsuits under BIPA and an investigation by the Privacy Commissioner of Canada for compliance with the Personal Information Protection and Electronic Documents Act (PIPEDA).
Bans on the use of facial recognition technology
United States of America
In May 2019, San Francisco, California became the first major United States city to ban the use of facial recognition software for police and other local government agencies' usage. San Francisco Supervisor, Aaron Peskin, introduced regulations that will require agencies to gain approval from the San Francisco Board of Supervisors to purchase surveillance technology. The regulations also require that agencies publicly disclose the intended use for new surveillance technology. In June 2019, Somerville, Massachusetts became the first city on the East Coast to ban face surveillance software for government use, specifically in police investigations and municipal surveillance. In July 2019, Oakland, California banned the usage of facial recognition technology by city departments.
The American Civil Liberties Union ("ACLU") has campaigned across the United States for transparency in surveillance technology and has supported both San Francisco and Somerville's ban on facial recognition software. The ACLU works to challenge the secrecy and surveillance with this technology.
During the George Floyd protests, use of facial recognition by city government was banned in Boston, Massachusetts. municipal use has been banned in:
Berkeley, California
Oakland, California
Boston, Massachusetts – June 30, 2020
Brookline, Massachusetts
Cambridge, Massachusetts
Northampton, Massachusetts
Springfield, Massachusetts
Somerville, Massachusetts
Portland, Oregon – September 2020
The West Lafayette, Indiana City Council passed an ordinance banning facial recognition surveillance technology.
On October 27, 2020, 22 human rights groups called upon the University of Miami to ban facial recognition technology. This came after the students accused the school of using the software to identify student protesters. The allegations were, however, denied by the university.
A state police reform law in Massachusetts will take effect in July 2021; a ban passed by the legislature was rejected by governor Charlie Baker. Instead, the law requires a judicial warrant, limit the personnel who can perform the search, record data about how the technology is used, and create a commission to make recommendations about future regulations.
Reports in 2024 revealed that some police departments, including San Francisco Police Department, had skirted bans on facial recognition technology that had been enacted in their respective cities.
European Union
In January 2020, the European Union suggested, but then quickly scrapped, a proposed moratorium on facial recognition in public spaces.
The European "Reclaim Your Face" coalition launched in October 2020. The coalition calls for a ban on facial recognition and launched a European Citizens' Initiative in February 2021. More than 60 organizations call on the European Commission to strictly regulate the use of biometric surveillance technologies.
Emotion recognition
In the 18th and 19th century, the belief that facial expressions revealed the moral worth or true inner state of a human was widespread and physiognomy was a respected science in the Western world. From the early 19th century onwards photography was used in the physiognomic analysis of facial features and facial expression to detect insanity and dementia. In the 1960s and 1970s the study of human emotions and its expressions was reinvented by psychologists, who tried to define a normal range of emotional responses to events. The research on automated emotion recognition has since the 1970s focused on facial expressions and speech, which are regarded as the two most important ways in which humans communicate emotions to other humans. In the 1970s the Facial Action Coding System (FACS) categorization for the physical expression of emotions was established. Its developer Paul Ekman maintains that there are six emotions that are universal to all human beings and that these can be coded in facial expressions. Research into automatic emotion specific expression recognition has in the past decades focused on frontal view images of human faces.
In 2016, facial feature emotion recognition algorithms were among the new technologies, alongside high-definition CCTV, high resolution 3D face recognition and iris recognition, that found their way out of university research labs. In 2016, Facebook acquired FacioMetrics, a facial feature emotion recognition corporate spin-off by Carnegie Mellon University. In the same year Apple Inc. acquired the facial feature emotion recognition start-up Emotient. By the end of 2016, commercial vendors of facial recognition systems offered to integrate and deploy emotion recognition algorithms for facial features. The MIT's Media Lab spin-off Affectiva by late 2019 offered a facial expression emotion detection product that can recognize emotions in humans while driving.
Anti-facial recognition systems
The development of anti-facial recognition technology is effectively an arms race between privacy researchers and big data companies. Big data companies increasingly use convolutional AI technology to create ever more advanced facial recognition models. Solutions to block facial recognition may not work on newer software, or on different types of facial recognition models. One popular cited example of facial-recognition blocking is the CVDazzle makeup and haircut system, but the creators note on their website that it has been outdated for quite some time as it was designed to combat a particular facial recognition algorithm and may not work. Another example is the emergence of facial recognition that can identify people wearing facemasks and sunglasses, especially after the COVID-19 pandemic.
Given that big data companies have much more funding than privacy researchers, it is very difficult for anti-facial recognition systems to keep up. There is also no guarantee that obfuscation techniques that were used for images taken in the past and stored, such as masks or software obfuscation, would protect users from facial-recognition analysis of those images by future technology.
In January 2013, Japanese researchers from the National Institute of Informatics created 'privacy visor' glasses that use nearly infrared light to make the face underneath it unrecognizable to face recognition software that use infrared. The latest version uses a titanium frame, light-reflective material and a mask which uses angles and patterns to disrupt facial recognition technology through both absorbing and bouncing back light sources. However, these methods are used to prevent infrared facial recognition and would not work on AI facial recognition of plain images. Some projects use adversarial machine learning to come up with new printed patterns that confuse existing face recognition software.
One method that may work to protect from facial recognition systems are specific haircuts and make-up patterns that prevent the used algorithms to detect a face, known as computer vision dazzle. Incidentally, the makeup styles popular with Juggalos may also protect against facial recognition.
Facial masks that are worn to protect from contagious viruses can reduce the accuracy of facial recognition systems. A 2020 NIST study, tested popular one-to-one matching systems and found a failure rate between five and fifty percent on masked individuals. The Verge speculated that the accuracy rate of mass surveillance systems, which were not included in the study, would be even less accurate than the accuracy of one-to-one matching systems. The facial recognition of Apple Pay can work through many barriers, including heavy makeup, thick beards and even sunglasses, but fails with masks. However, facial recognition of masked faces is increasingly getting more reliable.
Another solution is the application of obfuscation to images that may fool facial recognition systems while still appearing normal to a human user. These could be used for when images are posted online or on social media. However, as it is hard to remove images once they are on the internet, the obfuscation on these images may be defeated and the face of the user identified by future advances in technology. Two examples of this technique, developed in 2020, are the ANU's 'Camera Adversaria' camera app, and the University of Chicago's Fawkes image cloaking software algorithm which applies obfuscation to already taken photos. However, by 2021 the Fawkes obfuscation algorithm had already been specifically targeted by Microsoft Azure which changed its algorithm to lower Fawkes' effectiveness.
See also
AI effect
Amazon Rekognition
Applications of artificial intelligence
Artificial intelligence for video surveillance
Automatic number plate recognition
Biometric technology in access control
Coke Zero Facial Profiler
Computer processing of body language
Computer vision
DeepFace
FaceNet
Face perception
Face Recognition Grand Challenge
FindFace
Glasgow Face Matching Test
ISO/IEC 19794-5
MALINTENT
National biometric id card
Multimedia information retrieval
Multilinear subspace learning
Pattern recognition, analogy and case-based reasoning
Retinal scan
SenseTime
Super recognisers
Template matching
Three-dimensional face recognition
Vein matching
Gait analysis
Fawkes (image cloaking software)
Lists
List of computer vision topics
List of emerging technologiesOutline of artificial intelligence
References
Further reading
"The Face Detection Algorithm Set to Revolutionize Image Search" (Feb. 2015), MIT Technology Review
Interview with Alvaro Bedoya, executive director of the Center on Privacy & Technology at Georgetown Law and co-author of Perpetual Line Up: Unregulated Police Face Recognition in America.
Press, Eyal, "In Front of Their Faces: Does facial-recognition technology lead police to ignore contradictory evidence?", The New Yorker, 20 November 2023, pp. 20–26.
External links
A Photometric Stereo Approach to Face Recognition (master's thesis). The University of the West of England, Bristol.
Automatic identification and data capture
Machine learning task
Surveillance
Video surveillance | Facial recognition system | [
"Technology"
] | 14,114 | [
"Data",
"Automatic identification and data capture"
] |
602,456 | https://en.wikipedia.org/wiki/Gardening%20%28cryptanalysis%29 | In cryptanalysis, gardening is the act of encouraging a target to use known plaintext in an encrypted message, typically by performing some action the target is sure to report. It was a term used during World War II at the British Government Code and Cypher School at Bletchley Park, England, for schemes to entice the Germans to include particular words, which the British called "cribs", in their encrypted messages. This term presumably came from RAF minelaying missions, or "gardening" sorties. "Gardening" was standard RAF slang for sowing mines in rivers, ports and oceans from low heights, possibly because each sea area around the European coasts was given a code-name of flowers or vegetables.
The technique is claimed to have been most effective against messages produced by the German Navy's Enigma machines. If the Germans had recently swept a particular area for mines, and analysts at Bletchley Park were in need of some cribs, they might (and apparently did on several occasions) request that the area be mined again. This would hopefully evoke encrypted messages from the local command mentioning Minen (German for mines), the location, and perhaps messages also from the headquarters with minesweeping ships to assign to that location, mentioning the same. It worked often enough to try several times.
This crib-based decryption is usually not considered a chosen-plaintext attack, even though plain text effectively chosen by the British was injected into the ciphertext, because the choice was very limited and the cryptanalysts did not care what the crib was so long as they knew it. Most chosen-plaintext cryptanalysis requires very specific patterns (e.g. long repetitions of "AAA...", "BBB...", "CCC...", etc.) which could not be mistaken for normal messages. It does, however, show that the boundary between these two is somewhat fuzzy.
Another notable example occurred during the lead up to the Battle of Midway. U.S. cryptanalysts had decrypted numerous Japanese messages about a planned operation at "AF", but the code word "AF" came from a second location code book which was not known. Suspecting it was Midway island, they arranged for the garrison there to report in the clear about a breakdown of their desalination plant. A Japanese report about "AF" being short of fresh water soon followed, confirming the guess.
See also
Cryptanalysis of the Enigma
Known-plaintext attack
Notes
Cryptographic attacks
Bletchley Park | Gardening (cryptanalysis) | [
"Technology"
] | 540 | [
"Cryptographic attacks",
"Computer security exploits"
] |
602,480 | https://en.wikipedia.org/wiki/Frobenius%20theorem%20%28differential%20topology%29 | In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds.
Contact geometry studies 1-forms that maximally violates the assumptions of Frobenius' theorem. An example is shown on the right.
Introduction
One-form version
Suppose we are to find the trajectory of a particle in a subset of 3D space, but we do not know its trajectory formula. Instead, we know only that its trajectory satisfies , where are smooth functions of . Thus, our only certainty is that if at some moment in time the particle is at location , then its velocity at that moment is restricted within the plane with equation
In other words, we can draw a "local plane" at each point in 3D space, and we know that the particle's trajectory must be tangent to the local plane at all times.
If we have two equationsthen we can draw two local planes at each point, and their intersection is generically a line, allowing us to uniquely solve for the curve starting at any point. In other words, with two 1-forms, we can foliate the domain into curves.
If we have only one equation , then we might be able to foliate into surfaces, in which case, we can be sure that a curve starting at a certain surface must be restricted to wander within that surface. If not, then a curve starting at any point might end up at any other point in . One can imagine starting with a cloud of little planes, and quilting them together to form a full surface. The main danger is that, if we quilt the little planes two at a time, we might go on a cycle and return to where we began, but shifted by a small amount. If this happens, then we would not get a 2-dimensional surface, but a 3-dimensional blob. An example is shown in the diagram on the right.
If the one-form is integrable, then loops exactly close upon themselves, and each surface would be 2-dimensional. Frobenius' theorem states that this happens precisely when over all of the domain, where . The notation is defined in the article on one-forms.
During his development of axiomatic thermodynamics, Carathéodory proved that if is an integrable one-form on an open subset of , then for some scalar functions on the subset. This is usually called Carathéodory's theorem in axiomatic thermodynamics. One can prove this intuitively by first constructing the little planes according to , quilting them together into a foliation, then assigning each surface in the foliation with a scalar label. Now for each point , define to be the scalar label of the surface containing point .
Now, is a one-form that has exactly the same planes as . However, it has "even thickness" everywhere, while might have "uneven thickness". This can be fixed by a scalar scaling by , giving . This is illustrated on the right.
Multiple one-forms
In its most elementary form, the theorem addresses the problem of finding a maximal set of independent solutions of a regular system of first-order linear homogeneous partial differential equations. Let
be a collection of functions, with , and such that the matrix has rank r when evaluated at any point of . Consider the following system of partial differential equations for a function :
One seeks conditions on the existence of a collection of solutions such that the gradients are linearly independent.
The Frobenius theorem asserts that this problem admits a solution locally if, and only if, the operators satisfy a certain integrability condition known as involutivity. Specifically, they must satisfy relations of the form
for , and all functions u, and for some coefficients ckij(x) that are allowed to depend on x. In other words, the commutators must lie in the linear span of the at every point. The involutivity condition is a generalization of the commutativity of partial derivatives. In fact, the strategy of proof of the Frobenius theorem is to form linear combinations among the operators so that the resulting operators do commute, and then to show that there is a coordinate system for which these are precisely the partial derivatives with respect to .
From analysis to geometry
Even though the system is overdetermined there are typically infinitely many solutions. For example, the system of differential equations
clearly permits multiple solutions. Nevertheless, these solutions still have enough structure that they may be completely described. The first observation is that, even if f1 and f2 are two different solutions, the level surfaces of f1 and f2 must overlap. In fact, the level surfaces for this system are all planes in of the form , for a constant. The second observation is that, once the level surfaces are known, all solutions can then be given in terms of an arbitrary function. Since the value of a solution f on a level surface is constant by definition, define a function C(t) by:
Conversely, if a function is given, then each function f given by this expression is a solution of the original equation. Thus, because of the existence of a family of level surfaces, solutions of the original equation are in a one-to-one correspondence with arbitrary functions of one variable.
Frobenius' theorem allows one to establish a similar such correspondence for the more general case of solutions of (1). Suppose that are solutions of the problem (1) satisfying the independence condition on the gradients. Consider the level sets of as functions with values in . If is another such collection of solutions, one can show (using some linear algebra and the mean value theorem) that this has the same family of level sets but with a possibly different choice of constants for each set. Thus, even though the independent solutions of (1) are not unique, the equation (1) nonetheless determines a unique family of level sets. Just as in the case of the example, general solutions u of (1) are in a one-to-one correspondence with (continuously differentiable) functions on the family of level sets.
The level sets corresponding to the maximal independent solution sets of (1) are called the integral manifolds because functions on the collection of all integral manifolds correspond in some sense to constants of integration. Once one of these constants of integration is known, then the corresponding solution is also known.
Frobenius' theorem in modern language
The Frobenius theorem can be restated more economically in modern language. Frobenius' original version of the theorem was stated in terms of Pfaffian systems, which today can be translated into the language of differential forms. An alternative formulation, which is somewhat more intuitive, uses vector fields.
Formulation using vector fields
In the vector field formulation, the theorem states that a subbundle of the tangent bundle of a manifold is integrable (or involutive) if and only if it arises from a regular foliation. In this context, the Frobenius theorem relates integrability to foliation; to state the theorem, both concepts must be clearly defined.
One begins by noting that an arbitrary smooth vector field on a manifold defines a family of curves, its integral curves (for intervals ). These are the solutions of , which is a system of first-order ordinary differential equations, whose solvability is guaranteed by the Picard–Lindelöf theorem. If the vector field is nowhere zero then it defines a one-dimensional subbundle of the tangent bundle of , and the integral curves form a regular foliation of . Thus, one-dimensional subbundles are always integrable.
If the subbundle has dimension greater than one, a condition needs to be imposed.
One says that a subbundle of the tangent bundle is integrable (or involutive), if, for any two vector fields and taking values in , the Lie bracket takes values in as well. This notion of integrability need only be defined locally; that is, the existence of the vector fields and and their integrability need only be defined on subsets of .
Several definitions of foliation exist. Here we use the following:
Definition. A p-dimensional, class Cr foliation of an n-dimensional manifold M is a decomposition of M into a union of disjoint connected submanifolds {Lα}α∈A, called the leaves of the foliation, with the following property: Every point in M has a neighborhood U and a system of local, class Cr coordinates x=(x1, ⋅⋅⋅, xn) : U→Rn such that for each leaf Lα, the components of U ∩ Lα are described by the equations xp+1=constant, ⋅⋅⋅, xn=constant. A foliation is denoted by ={Lα}α∈A.
Trivially, any foliation of defines an integrable subbundle, since if and is the leaf of the foliation passing through then is integrable. Frobenius' theorem states that the converse is also true:
Given the above definitions, Frobenius' theorem states that a subbundle is integrable if and only if the subbundle arises from a regular foliation of .
Differential forms formulation
Let U be an open set in a manifold , be the space of smooth, differentiable 1-forms on U, and F be a submodule of of rank r, the rank being constant in value over U. The Frobenius theorem states that F is integrable if and only if for every in the stalk Fp is generated by r exact differential forms.
Geometrically, the theorem states that an integrable module of -forms of rank r is the same thing as a codimension-r foliation. The correspondence to the definition in terms of vector fields given in the introduction follows from the close relationship between differential forms and Lie derivatives. Frobenius' theorem is one of the basic tools for the study of vector fields and foliations.
There are thus two forms of the theorem: one which operates with distributions, that is smooth subbundles D of the tangent bundle TM; and the other which operates with subbundles of the graded ring of all forms on M. These two forms are related by duality. If D is a smooth tangent distribution on , then the annihilator of D, I(D) consists of all forms (for any ) such that
for all . The set I(D) forms a subring and, in fact, an ideal in . Furthermore, using the definition of the exterior derivative, it can be shown that I(D) is closed under exterior differentiation (it is a differential ideal) if and only if D is involutive. Consequently, the Frobenius theorem takes on the equivalent form that is closed under exterior differentiation if and only if D is integrable.
Generalizations
The theorem may be generalized in a variety of ways.
Infinite dimensions
One infinite-dimensional generalization is as follows. Let and be Banach spaces, and a pair of open sets. Let
be a continuously differentiable function of the Cartesian product (which inherits a differentiable structure from its inclusion into X ×Y ) into the space of continuous linear transformations of into Y. A differentiable mapping u : A → B is a solution of the differential equation
if
The equation (1) is completely integrable if for each , there is a neighborhood U of x0 such that (1) has a unique solution defined on U such that u(x0)=y0.
The conditions of the Frobenius theorem depend on whether the underlying field is or . If it is R, then assume F is continuously differentiable. If it is , then assume F is twice continuously differentiable. Then (1) is completely integrable at each point of if and only if
for all . Here (resp. ) denotes the partial derivative with respect to the first (resp. second) variable; the dot product denotes the action of the linear operator , as well as the actions of the operators and .
Banach manifolds
The infinite-dimensional version of the Frobenius theorem also holds on Banach manifolds. The statement is essentially the same as the finite-dimensional version.
Let be a Banach manifold of class at least C2. Let be a subbundle of the tangent bundle of . The bundle is involutive if, for each point and pair of sections and Y of defined in a neighborhood of p, the Lie bracket of and Y evaluated at p, lies in :
On the other hand, is integrable if, for each , there is an immersed submanifold whose image contains p, such that the differential of is an isomorphism of TN with .
The Frobenius theorem states that a subbundle is integrable if and only if it is involutive.
Holomorphic forms
The statement of the theorem remains true for holomorphic 1-forms on complex manifolds — manifolds over with biholomorphic transition functions.
Specifically, if are r linearly independent holomorphic 1-forms on an open set in such that
for some system of holomorphic 1-forms , then there exist holomorphic functions fij and such that, on a possibly smaller domain,
This result holds locally in the same sense as the other versions of the Frobenius theorem. In particular, the fact that it has been stated for domains in is not restrictive.
Higher degree forms
The statement does not generalize to higher degree forms, although there is a number of partial results such as Darboux's theorem and the Cartan-Kähler theorem.
History
Despite being named for Ferdinand Georg Frobenius, the theorem was first proven by Alfred Clebsch and Feodor Deahna. Deahna was the first to establish the sufficient conditions for the theorem, and Clebsch developed the necessary conditions. Frobenius is responsible for applying the theorem to Pfaffian systems, thus paving the way for its usage in differential topology.
Applications
In classical mechanics, the integrability of a system's constraint equations determines whether the system is holonomic or nonholonomic.
In microeconomic theory, Frobenius' theorem can be used to prove the existence of a solution to the problem of integrability of demand functions.
Carathéodory's axiomatic thermodynamics
In classical thermodynamics, Frobenius' theorem can be used to construct entropy and temperature in Carathéodory's formalism.
Specifically, Carathéodory considered a thermodynamic system (concretely one can imagine a piston of gas) that can interact with the outside world by either heat conduction (such as setting the piston on fire) or mechanical work (pushing on the piston). He then defined "adiabatic process" as any process that the system may undergo without heat conduction, and defined a relation of "adiabatic accessibility" thus: if the system can go from state A to state B after an adiabatic process, then is adiabatically accessible from . Write it as .
Now assume that
For any pair of states , at least one of and holds.
For any state , and any neighborhood of , there exists a state in the neighborhood, such that is adiabatically inaccessible from .
Then, we can foliate the state space into subsets of states that are mutually adiabatically accessible. With mild assumptions on the smoothness of , each subset is a manifold of codimension 1. Call these manifolds "adiabatic surfaces".
By the first law of thermodynamics, there exists a scalar function ("internal energy") on the state space, such thatwhere are the possible ways to perform mechanical work on the system. For example, if the system is a tank of ideal gas, then .
Now, define the one-form on the state spaceNow, since the adiabatic surfaces are tangent to at every point in state space, is integrable, so by Carathéodory's theorem, there exists two scalar functions on state space, such that . These are the temperature and entropy functions, up to a multiplicative constant.
By plugging in the ideal gas laws, and noting that Joule expansion is an (irreversible) adiabatic process, we can fix the sign of , and find that means . That is, entropy is preserved in reversible adiabatic processes, and increases during irreversible adiabatic processes.
See also
Integrability conditions for differential systems
Domain-straightening theorem
Newlander-Nirenberg Theorem
Notes
References
Theorems in differential geometry
Theorems in differential topology
Differential systems
Foliations | Frobenius theorem (differential topology) | [
"Mathematics"
] | 3,607 | [
"Theorems in differential geometry",
"Theorems in topology",
"Theorems in differential topology",
"Theorems in geometry"
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602,490 | https://en.wikipedia.org/wiki/Sober%20space | In mathematics, a sober space is a topological space X such that every (nonempty) irreducible closed subset of X is the closure of exactly one point of X: that is, every nonempty irreducible closed subset has a unique generic point.
Definitions
Sober spaces have a variety of cryptomorphic definitions, which are documented in this section . In each case below, replacing "unique" with "at most one" gives an equivalent formulation of the T0 axiom. Replacing it with "at least one" is equivalent to the property that the T0 quotient of the space is sober, which is sometimes referred to as having "enough points" in the literature.
With irreducible closed sets
A closed set is irreducible if it cannot be written as the union of two proper closed subsets. A space is sober if every nonempty irreducible closed subset is the closure of a unique point.
In terms of morphisms of frames and locales
A topological space X is sober if every map that preserves all joins and all finite meets from its partially ordered set of open subsets to is the inverse image of a unique continuous function from the one-point space to X.
This may be viewed as a correspondence between the notion of a point in a locale and a point in a topological space, which is the motivating definition.
Using completely prime filters
A filter F of open sets is said to be completely prime if for any family of open sets such that , we have that for some i. A space X is sober if each completely prime filter is the neighbourhood filter of a unique point in X.
In terms of nets
A net is self-convergent if it converges to every point in , or equivalently if its eventuality filter is completely prime. A net that converges to converges strongly if it can only converge to points in the closure of . A space is sober if every self-convergent net converges strongly to a unique point .
In particular, a space is T1 and sober precisely if every self-convergent net is constant.
As a property of sheaves on the space
A space X is sober if every functor from the category of sheaves Sh(X) to Set that preserves all finite limits and all small colimits must be the stalk functor of a unique point x.
Properties and examples
Any Hausdorff (T2) space is sober (the only irreducible subsets being points), and all sober spaces are Kolmogorov (T0), and both implications are strict.
Sobriety is not comparable to the T1 condition:
an example of a T1 space which is not sober is an infinite set with the cofinite topology, the whole space being an irreducible closed subset with no generic point;
an example of a sober space which is not T1 is the Sierpinski space.
Moreover T2 is stronger than T1 and sober, i.e., while every T2 space is at once T1 and sober, there exist spaces that are simultaneously T1 and sober, but not T2. One such example is the following: let X be the set of real numbers, with a new point p adjoined; the open sets being all real open sets, and all cofinite sets containing p.
Sobriety of X is precisely a condition that forces the lattice of open subsets of X to determine X up to homeomorphism, which is relevant to pointless topology.
Sobriety makes the specialization preorder a directed complete partial order.
Every continuous directed complete poset equipped with the Scott topology is sober.
Finite T0 spaces are sober.
The prime spectrum Spec(R) of a commutative ring R with the Zariski topology is a compact sober space. In fact, every spectral space (i.e. a compact sober space for which the collection of compact open subsets is closed under finite intersections and forms a base for the topology) is homeomorphic to Spec(R) for some commutative ring R. This is a theorem of Melvin Hochster.
More generally, the underlying topological space of any scheme is a sober space.
The subset of Spec(R) consisting only of the maximal ideals, where R is a commutative ring, is not sober in general.
See also
Stone duality, on the duality between topological spaces that are sober and frames (i.e. complete Heyting algebras) that are spatial.
References
Further reading
General topology
Separation axioms
Properties of topological spaces | Sober space | [
"Mathematics"
] | 929 | [
"General topology",
"Properties of topological spaces",
"Space (mathematics)",
"Topological spaces",
"Topology"
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602,528 | https://en.wikipedia.org/wiki/Great%20Falls%20%28Passaic%20River%29 | The Great Falls of the Passaic River is a prominent waterfall, high, on the Passaic River in the city of Paterson in Passaic County, New Jersey. One of the United States' largest waterfalls, it played a significant role in the early industrial development of New Jersey starting in the earliest days of the nation. The falls and surrounding area are protected as part of the Paterson Great Falls National Historical Park, administered by the National Park Service. Congress authorized its establishment in 2009.
In 1967 it was designated a National Natural Landmark together with Garret Mountain Reservation. The falls and the surrounding neighborhood have also been designated as a National Historic Landmark District since 1976. The Great Falls' raceway and power systems were designated a National Historic Civil Engineering Landmark and a National Historic Mechanical Engineering Landmark in 1977.
History
Formation and early history
Geologically, the falls were formed at the end of the last ice age approximately 13,000 years ago. Formerly the Passaic had followed a shorter course through the Watchung Mountains near present-day Summit. As the glacier receded, the river's previous course was blocked by a newly formed moraine. A large lake, called Glacial Lake Passaic, formed behind the Watchungs. As the ice receded, the river found a new circuitous route around the north end of the Watchungs, carving the spectacular falls through the underlying basalt, which was formed approximately 200 million years ago.
The falls later became the site of a habitation of the historic Lenape Native Americans, who followed earlier indigenous cultures in the region. Later, in the colonial era, Dutch settlers developed a community here beginning in the 1690s.
Industrial development
In 1778, Alexander Hamilton visited the falls and was impressed by its potential for industry. Later when Hamilton was the nation's Secretary of Treasury, he selected the site of the nation's first planned industrial city, which he called a "national manufactory." In 1791, Hamilton helped found the Society for the Establishment of Useful Manufactures (S.U.M.), a state-chartered private corporation to fulfill this vision. The town of Paterson was founded by the society and named after New Jersey Governor William Paterson, in appreciation of his efforts to promote the society.
Hamilton commissioned civil engineer Pierre Charles L'Enfant, responsible for the layout of the new capital at Washington, D.C., to design the system of canals known as raceways to supply the power for the watermills in the new town. As a result, Paterson became the nucleus for a burgeoning mill industry. In 1792, David Godwin was commissioned to build the first water-powered cotton spinning mill in New Jersey. He subsequently built the first dam on the falls; it was a structure made of wood.
In 1812, this was the site of the state's first continuous roll paper mill. Other 19th-century industries that produced goods using the falls as a power source include the Rogers Locomotive Works (1832), Colt's Manufacturing Company, for the Colt revolver (1837), and the construction of the USS Holland (SS-1) (1898). The oldest extant structure in the historic district is the Phoenix Mill, built in 1813.
Workers were exploited, especially new immigrants from Europe, who often did not speak English. They began to seek better working conditions. The industrial area became the site of labor unrest, and it was a center for the 1913 Paterson silk strike. Facing harsh conditions in factories, immigrant workers staged numerous strikes during and after the Great War, adding to social tensions of the time. They organized the first labor movements in the United States.
The SUM society continued operation until 1945, when its charter and property were sold to the city of Paterson. The area fell into disuse during a period of restructuring that resulted in a steep decline of industry in the region during the mid to late 20th century. In 1971, concerned residents established the Great Falls Preservation and Development Corporation to restore and redevelop the historic mill buildings and raceways as artifacts of industrial history.
Great Falls State Park
The State of New Jersey announced plans for a new urban state park in Paterson surrounding the Great Falls, called Great Falls State Park, in 2007. The master plan for the park called for utilizing surrounding industrial areas for parklands that include a trail network and recreation areas, and creating new areas to view the falls. These plans were superseded by the establishment of Great Falls National Historical Park.
National Historical Park
On March 30, 2009, President Obama signed the Omnibus Public Land Management Act authorizing the falls as a national historical park, which would provide additional federal protections for the 77-foot waterfall. By 2011, Great Falls State Park and other land along the Passaic River were transferred to the federal government for the creation of the Paterson Great Falls National Historical Park. Formal establishment as a unit of the National Park System required action by the Secretary of the Interior, which took place November 7, 2011, when Secretary Salazar formally accepted lands on behalf of the United States, and dedicated the park as the nation's 397th park system unit.
Viewing the falls
The Falls are viewable from Haines Overlook Park on the south and Mary Ellen Kramer Park on the north. Drive-by viewing is available from McBride Avenue where it crosses the river just above the Falls. A footbridge over the Falls gorge (historically, the eighth such bridge to span this chasm) also serves as an outlook point. A visitor's center at the corner of Spruce and McBride avenues, in the Great Falls Historic District, provides a historical overview of the falls and the industrial and cultural history of Paterson. A record 177,000 visitors went to the Great Falls in 2016.
National Natural Landmark
The Great Falls of Paterson – Garret Mountain is a National Natural Landmark designated in January 1967 and expanded in April 1967 to include nearby Garret Mountain. Together they help demonstrate how jointed basaltic lava flow shaped the geology of the area during the Early Mesozoic period through both extrusion and intrusion.
The designation protects the site from federal development, but not from local and state development. Redevelopment of the decayed adjacent industrial areas has been an ongoing controversial topic. An attempt in the 1990s to redevelop the adjacent Allied Textile Printing Co. (ATP) facility, destroyed by fire in the 1980s, into prefabricated townhouses was initially approved by the city but later repelled by a coalition of local citizens seeking to preserve the historic character of the district.
Hydroelectric facility
The hydroelectric plant at the falls is operated by Eagle Creek Renewable Energy, which is considering commissioning another facility downstream at the Dundee Dam.
The Great Falls hydroelectric plant has three Kaplan type turbines with a total capacity of 10.95 Mwe. Flow through each turbine is 710 cfs, with a total flow of 2,130 cfs, 1,377 MGD. Three 8.5' diameter penstocks feed the turbines, with a velocity 12.5 ft/sec and 8.5 mph.
In popular culture
The unique history of the Great Falls and the city were described in the five-volume philosophical poem Paterson by William Carlos Williams. Among the episodes described in Williams' poem is the 1827 leap over the falls by Sam Patch, who later became the first known person to perform a stunt at Niagara Falls. The 2016 film Paterson, directed by Jim Jarmusch, is partly inspired by the works of Williams and features the falls as a primary location.
The Great Falls were also featured in the pilot of the HBO crime drama The Sopranos, as well as in the series' sixth episode, in which Mikey Palmice and another associate throw a drug dealer off the bridge and into the falls to his death.
See also
List of waterfalls
List of National Natural Landmarks in New Jersey
Garret Mountain Reservation
National Register of Historic Places listings in Passaic County, New Jersey
Paterson Museum and Rogers Locomotive and Machine Works
Old Great Falls Historic District
Lambert Castle
References
External links
Paterson Great Falls National Historical Park
National Park Service: On Designation of the Area as part of the National Park System
Paterson Friends of the Great Falls
Passaic County, NJ Passaic County Board of Chosen Freeholders
Hamilton Partnership for Paterson
From Local Landmark to National Site
Landforms of Passaic County, New Jersey
Historic Civil Engineering Landmarks
Historic districts on the National Register of Historic Places in New Jersey
National Historic Landmarks in New Jersey
National Historical Parks in New Jersey
Passaic River
National Natural Landmarks in New Jersey
Protected areas of Passaic County, New Jersey
Watchung Mountains
Waterfalls of New Jersey
Parks in Passaic County, New Jersey
National Register of Historic Places in Passaic County, New Jersey
Block waterfalls
Protected areas established in 2009
2009 establishments in New Jersey
United Water
Paterson, New Jersey
Hydroelectric power plants in New Jersey
Energy infrastructure on the National Register of Historic Places
Geography of Passaic County, New Jersey
National historical parks of the United States | Great Falls (Passaic River) | [
"Engineering"
] | 1,798 | [
"Civil engineering",
"Historic Civil Engineering Landmarks"
] |
602,616 | https://en.wikipedia.org/wiki/Quaternary%20sector%20of%20the%20economy | The quaternary sector of the economy is based upon the economic activity that is associated with either the intellectual or knowledge-based economy. This consists of information technology; media; research and development; information-based services such as information-generation and information-sharing; and knowledge-based services such as consultation, entertainment, broadcasting, mass media, telecommunication, education, information technology, financial planning, blogging, and designing.
Other definitions describe the quaternary sector as pure services. This may consist of the entertainment industry, to describe media and culture, and government. This may be classified into an additional quinary sector.
The term reflects the analysis of the three-sector model of the economy, in which the primary sector produces raw materials used by the secondary sector to produce goods, which are then distributed to consumers by the tertiary sector.
Contrary to this implied sequence, however, the quaternary sector does not process the output of the tertiary sector. It has only limited and indirect connections to the industrial economy characterized by the three-sector model.
In a modern economy, the generation, analysis and dissemination of information is important enough to warrant a separate sector instead of being a part of the tertiary sector. This sector evolves in well-developed countries where the primary and secondary sectors are a minority of the economy, and requires a highly educated workforce.
For example, the tertiary and quaternary sectors form the largest part of the UK economy, employing 76% of the workforce.
See also
Indigo Era
Economic Sector
Economic sector#:~:text=One classical breakdown of economic,work in the tertiary sector.
Outline of industry#:~:text=Industry sectors * Primary sector of the,Quinary sector of the economy (humanitarian services)
References
+4
National accounts | Quaternary sector of the economy | [
"Technology"
] | 356 | [
"Economic sectors",
"Components"
] |
602,650 | https://en.wikipedia.org/wiki/Type%20safety | In computer science, type safety and type soundness are the extent to which a programming language discourages or prevents type errors. Type safety is sometimes alternatively considered to be a property of facilities of a computer language; that is, some facilities are type-safe and their usage will not result in type errors, while other facilities in the same language may be type-unsafe and a program using them may encounter type errors. The behaviors classified as type errors by a given programming language are usually those that result from attempts to perform operations on values that are not of the appropriate data type, e.g., adding a string to an integer when there's no definition on how to handle this case. This classification is partly based on opinion.
Type enforcement can be static, catching potential errors at compile time, or dynamic, associating type information with values at run-time and consulting them as needed to detect imminent errors, or a combination of both. Dynamic type enforcement often allows programs to run that would be invalid under static enforcement.
In the context of static (compile-time) type systems, type safety usually involves (among other things) a guarantee that the eventual value of any expression will be a legitimate member of that expression's static type. The precise requirement is more subtle than this — see, for example, subtyping and polymorphism for complications.
Definitions
Intuitively, type soundness is captured by Robin Milner's pithy statement that
Well-typed programs cannot "go wrong".
In other words, if a type system is sound, then expressions accepted by that type system must evaluate to a value of the appropriate type (rather than produce a value of some other, unrelated type or crash with a type error). Vijay Saraswat provides the following, related definition:
A language is type-safe if the only operations that can be performed on data in the language are those sanctioned by the type of the data.
However, what precisely it means for a program to be "well typed" or to "go wrong" are properties of its static and dynamic semantics, which are specific to each programming language. Consequently, a precise, formal definition of type soundness depends upon the style of formal semantics used to specify a language. In 1994, Andrew Wright and Matthias Felleisen formulated what has become the standard definition and proof technique for type safety in languages defined by operational semantics, which is closest to the notion of type safety as understood by most programmers. Under this approach, the semantics of a language must have the following two properties to be considered type-sound:
Progress A well-typed program never gets "stuck": every expression is either already a value or can be reduced towards a value in some well-defined way. In other words, the program never gets into an undefined state where no further transitions are possible.
Preservation (or subject reduction) After each evaluation step, the type of each expression remains the same (that is, its type is preserved).
A number of other formal treatments of type soundness have also been published in terms of denotational semantics and structural operational semantics.
Relation to other forms of safety
In isolation, type soundness is a relatively weak property, as it essentially just states that the rules of a type system are internally consistent and cannot be subverted. However, in practice, programming languages are designed so that well-typedness also entails other, stronger properties, some of which include:
Prevention of illegal operations. For example, a type system can reject the expression 3 / "Hello, World" as invalid, because the division operator is not defined for a string divisor.
Memory safety
Type systems can prevent wild pointers that could otherwise arise from a pointer to one type of object being treated as a pointer to another type.
More sophisticated type systems, such as those supporting dependent types, can detect and reject out-of-bound accesses, preventing potential buffer overflows.
Logic errors originating in the semantics of different types. For instance, inches and millimeters may both be stored as integers, but should not be substituted for each other or added. A type system can enforce two different types of integer for them.
Type-safe and type-unsafe languages
Type safety is usually a requirement for any toy language (i.e. esoteric language) proposed in academic programming language research. Many languages, on the other hand, are too big for human-generated type safety proofs, as they often require checking thousands of cases. Nevertheless, some languages such as Standard ML, which has rigorously defined semantics, have been proved to meet one definition of type safety. Some other languages such as Haskell are believed to meet some definition of type safety, provided certain "escape" features are not used (for example Haskell's , used to "escape" from the usual restricted environment in which I/O is possible, circumvents the type system and so can be used to break type safety.) Type punning is another example of such an "escape" feature. Regardless of the properties of the language definition, certain errors may occur at run-time due to bugs in the implementation, or in linked libraries written in other languages; such errors could render a given implementation type unsafe in certain circumstances. An early version of Sun's Java virtual machine was vulnerable to this sort of problem.
Strong and weak typing
Programming languages are often colloquially classified as strongly typed or weakly typed (also loosely typed) to refer to certain aspects of type safety. In 1974, Liskov and Zilles defined a strongly-typed language as one in which "whenever an object is passed from a calling function to a called function, its type must be compatible with the type declared in the called function."
In 1977, Jackson wrote, "In a strongly typed language each data area will have a distinct type and each process will state its communication requirements in terms of these types."
In contrast, a weakly typed language may produce unpredictable results or may perform implicit type conversion.
Memory management and type safety
Type safety is closely linked to memory safety. For instance, in an implementation of a language that has some type which allows some bit patterns but not others, a dangling pointer memory error allows writing a bit pattern that does not represent a legitimate member of into a dead variable of type , causing a type error when the variable is read. Conversely, if the language is memory-safe, it cannot allow an arbitrary integer to be used as a pointer, hence there must be a separate pointer or reference type.
As a minimal condition, a type-safe language must not allow dangling pointers across allocations of different types. But most languages enforce the proper use of abstract data types defined by programmers even when this is not strictly necessary for memory safety or for the prevention of any kind of catastrophic failure. Allocations are given a type describing its contents, and this type is fixed for the duration of the allocation. This allows type-based alias analysis to infer that allocations of different types are distinct.
Most type-safe languages use garbage collection. Pierce says, "it is extremely difficult to achieve type safety in the presence of an explicit deallocation operation", due to the dangling pointer problem. However Rust is generally considered type-safe and uses a borrow checker to achieve memory safety, instead of garbage collection.
Type safety in object oriented languages
In object oriented languages type safety is usually intrinsic in the fact that a type system is in place. This is expressed in terms of class definitions.
A class essentially defines the structure of the objects derived from it and an API as a contract for handling these objects.
Each time a new object is created it will comply with that contract.
Each function that exchanges objects derived from a specific class, or implementing a specific interface, will adhere to that contract: hence in that function the operations permitted on that object will be only those defined by the methods of the class the object implements.
This will guarantee that the object integrity will be preserved.
Exceptions to this are object oriented languages that allow dynamic modification of the object structure, or the use of reflection to modify the content of an object to overcome the constraints imposed by the class methods definitions.
Type safety issues in specific languages
Ada
Ada was designed to be suitable for embedded systems, device drivers and other forms of system programming, but also to encourage type-safe programming. To resolve these conflicting goals, Ada confines type-unsafety to a certain set of special constructs whose names usually begin with the string . Unchecked_Deallocation can be effectively banned from a unit of Ada text by applying to this unit. It is expected that programmers will use constructs very carefully and only when necessary; programs that do not use them are type-safe.
The SPARK programming language is a subset of Ada eliminating all its potential ambiguities and insecurities while at the same time adding statically checked contracts to the language features available. SPARK avoids the issues with dangling pointers by disallowing allocation at run time entirely.
Ada2012 adds statically checked contracts to the language itself (in form of pre-, and post-conditions, as well as type invariants).
C
The C programming language is type-safe in limited contexts; for example, a compile-time error is generated when an attempt is made to convert a pointer to one type of structure to a pointer to another type of structure, unless an explicit cast is used. However, a number of very common operations are non-type-safe; for example, the usual way to print an integer is something like printf("%d", 12), where the %d tells printf at run-time to expect an integer argument. (Something like printf("%s", 12), which tells the function to expect a pointer to a character-string and yet supplies an integer argument, may be accepted by compilers, but will produce undefined results.) This is partially mitigated by some compilers (such as gcc) checking type correspondences between printf arguments and format strings.
In addition, C, like Ada, provides unspecified or undefined explicit conversions; and unlike in Ada, idioms that use these conversions are very common, and have helped to give C a type-unsafe reputation. For example, the standard way to allocate memory on the heap is to invoke a memory allocation function, such as malloc, with an argument indicating how many bytes are required. The function returns an untyped pointer (type void *), which the calling code must explicitly or implicitly cast to the appropriate pointer type. Pre-standardized implementations of C required an explicit cast to do so, therefore the code (struct foo *) malloc(sizeof(struct foo)) became the accepted practice.
C++
Some features of C++ that promote more type-safe code:
The new operator returns a pointer of type based on operand, whereas malloc returns a void pointer.
C++ code can use virtual functions and templates to achieve polymorphism without void pointers.
Safer casting operators, such as dynamic cast that performs run-time type checking.
C++11 strongly-typed enumerations cannot be implicitly converted to or from integers or other enumeration types.
C++ explicit constructors and C++11 explicit conversion operators prevent implicit type conversions.
C#
C# is type-safe. It has support for untyped pointers, but this must be accessed using the "unsafe" keyword which can be prohibited at the compiler level. It has inherent support for run-time cast validation. Casts can be validated by using the "as" keyword that will return a null reference if the cast is invalid, or by using a C-style cast that will throw an exception if the cast is invalid. See C Sharp conversion operators.
Undue reliance on the object type (from which all other types are derived) runs the risk of defeating the purpose of the C# type system. It is usually better practice to abandon object references in favour of generics, similar to templates in C++ and generics in Java.
Java
The Java language is designed to enforce type safety.
Anything in Java happens inside an object
and each object is an instance of a class.
To implement the type safety enforcement, each object, before usage, needs to be allocated.
Java allows usage of primitive types but only inside properly allocated objects.
Sometimes a part of the type safety is implemented indirectly: e.g. the class BigDecimal represents a floating point number of arbitrary precision, but handles only numbers that can be expressed with a finite representation.
The operation BigDecimal.divide() calculates a new object as the division of two numbers expressed as BigDecimal.
In this case if the division has no finite representation, as when one computes e.g. 1/3=0.33333..., the divide() method can raise an exception if no rounding mode is defined for the operation.
Hence the library, rather than the language, guarantees that the object respects the contract implicit in the class definition.
Standard ML
Standard ML has rigorously defined semantics and is known to be type-safe. However, some implementations, including Standard ML of New Jersey (SML/NJ), its syntactic variant Mythryl and MLton, provide libraries that offer unsafe operations. These facilities are often used in conjunction with those implementations' foreign function interfaces to interact with non-ML code (such as C libraries) that may require data laid out in specific ways. Another example is the SML/NJ interactive toplevel itself, which must use unsafe operations to execute ML code entered by the user.
Modula-2
Modula-2 is a strongly-typed language with a design philosophy to require any unsafe facilities to be explicitly marked as unsafe. This is achieved by "moving" such facilities into a built-in pseudo-library called SYSTEM from where they must be imported before they can be used. The import thus makes it visible when such facilities are used. Unfortunately, this was not consequently implemented in the original language report and its implementation. There still remained unsafe facilities such as the type cast syntax and variant records (inherited from Pascal) that could be used without prior import. The difficulty in moving these facilities into the SYSTEM pseudo-module was the lack of any identifier for the facility that could then be imported since only identifiers can be imported, but not syntax.
IMPORT SYSTEM; (* allows the use of certain unsafe facilities: *)
VAR word : SYSTEM.WORD; addr : SYSTEM.ADDRESS;
addr := SYSTEM.ADR(word);
(* but type cast syntax can be used without such import *)
VAR i : INTEGER; n : CARDINAL;
n := CARDINAL(i); (* or *) i := INTEGER(n);
The ISO Modula-2 standard corrected this for the type cast facility by changing the type cast syntax into a function called CAST which has to be imported from pseudo-module SYSTEM. However, other unsafe facilities such as variant records remained available without any import from pseudo-module SYSTEM.
IMPORT SYSTEM;
VAR i : INTEGER; n : CARDINAL;
i := SYSTEM.CAST(INTEGER, n); (* Type cast in ISO Modula-2 *)
A recent revision of the language applied the original design philosophy rigorously. First, pseudo-module SYSTEM was renamed to UNSAFE to make the unsafe nature of facilities imported from there more explicit. Then all remaining unsafe facilities where either removed altogether (for example variant records) or moved to pseudo-module UNSAFE. For facilities where there is no identifier that could be imported, enabling identifiers were introduced. In order to enable such a facility, its corresponding enabling identifier must be imported from pseudo-module UNSAFE. No unsafe facilities remain in the language that do not require import from UNSAFE.
IMPORT UNSAFE;
VAR i : INTEGER; n : CARDINAL;
i := UNSAFE.CAST(INTEGER, n); (* Type cast in Modula-2 Revision 2010 *)
FROM UNSAFE IMPORT FFI; (* enabling identifier for foreign function interface facility *)
<*FFI="C"*> (* pragma for foreign function interface to C *)
Pascal
Pascal has had a number of type safety requirements, some of which are kept in some compilers. Where a Pascal compiler dictates "strict typing", two variables cannot be assigned to each other unless they are either compatible (such as conversion of integer to real) or assigned to the identical subtype. For example, if you have the following code fragment:
type
TwoTypes = record
I: Integer;
Q: Real;
end;
DualTypes = record
I: Integer;
Q: Real;
end;
var
T1, T2: TwoTypes;
D1, D2: DualTypes;
Under strict typing, a variable defined as is not compatible with (because they are not identical, even though the components of that user defined type are identical) and an assignment of T1 := D2; is illegal. An assignment of T1 := T2; would be legal because the subtypes they are defined to are identical. However, an assignment such as T1.Q := D1.Q; would be legal.
Common Lisp
In general, Common Lisp is a type-safe language. A Common Lisp compiler is responsible for inserting dynamic checks for operations whose type safety cannot be proven statically. However, a programmer may indicate that a program should be compiled with a lower level of dynamic type-checking. A program compiled in such a mode cannot be considered type-safe.
C++ examples
The following examples illustrates how C++ cast operators can break type safety when used incorrectly. The first example shows how basic data types can be incorrectly cast:
#include <iostream>
using namespace std;
int main () {
int ival = 5; // integer value
float fval = reinterpret_cast<float&>(ival); // reinterpret bit pattern
cout << fval << endl; // output integer as float
return 0;
}
In this example, reinterpret_cast explicitly prevents the compiler from performing a safe conversion from integer to floating-point value. When the program runs it will output a garbage floating-point value. The problem could have been avoided by instead writing float fval = ival;
The next example shows how object references can be incorrectly downcast:
#include <iostream>
using namespace std;
class Parent {
public:
virtual ~Parent() {} // virtual destructor for RTTI
};
class Child1 : public Parent {
public:
int a;
};
class Child2 : public Parent {
public:
float b;
};
int main () {
Child1 c1;
c1.a = 5;
Parent & p = c1; // upcast always safe
Child2 & c2 = static_cast<Child2&>(p); // invalid downcast
cout << c2.b << endl; // will output garbage data
return 0;
}
The two child classes have members of different types. When downcasting a parent class pointer to a child class pointer, then the resulting pointer may not point to a valid object of correct type. In the example, this leads to garbage value being printed. The problem could have been avoided by replacing static_cast with dynamic_cast that throws an exception on invalid casts.
See also
Type theory
Notes
References
Programming language topics
Type theory
Articles with example Pascal code | Type safety | [
"Mathematics",
"Engineering"
] | 4,026 | [
"Mathematical structures",
"Mathematical logic",
"Mathematical objects",
"Type theory",
"Software engineering",
"Programming language topics"
] |
602,678 | https://en.wikipedia.org/wiki/Extraterrestrial%20sky | In astronomy, an extraterrestrial sky is a view of outer space from the surface of an astronomical body other than Earth.
The only extraterrestrial sky that has been directly observed and photographed by astronauts is that of the Moon. The skies of Venus, Mars and Titan have been observed by space probes designed to land on the surface and transmit images back to Earth.
Characteristics of extraterrestrial sky appear to vary substantially due to a number of factors. An extraterrestrial atmosphere, if present, has a large bearing on visible characteristics. The atmosphere's density and chemical composition can contribute to differences in color, opacity (including haze) and the presence of clouds. Astronomical objects may also be visible and can include natural satellites, rings, star systems and nebulas and other planetary system bodies.
Luminosity and angular diameter of the Sun
The Sun's apparent magnitude changes according to the inverse square law, therefore, the difference in magnitude as a result of greater or lesser distances from different celestial bodies can be predicted by the following formula:
Where "distance" can be in km, AU, or any other appropriate unit.
To illustrate, since Pluto is 40 AU away from the Sun on average, it follows that the parent star would appear to be times as bright as it is on Earth.
Though a terrestrial observer would find a dramatic decrease in available sunlight in these environments, the Sun would still be bright enough to cast shadows even as far as the hypothetical Planet Nine, possibly located 1,200 AU away, and by analogy would still outshine the full Moon as seen from Earth.
The change in angular diameter of the Sun with distance is illustrated in the diagram below:
The angular diameter of a circle whose plane is perpendicular to the displacement vector between the point of view and the centre of said circle can be calculated using the formula
in which is the angular diameter, and and are the actual diameter of and the distance to the object. When , we have , and the result obtained is in radians.
For a spherical object whose actual diameter equals and where is the distance to the centre of the sphere, the angular diameter can be found by the formula
The difference is due to the fact that the apparent edges of a sphere are its tangent points, which are closer to the observer than the centre of the sphere. For practical use, the distinction is significant only for spherical objects that are relatively close, since the small-angle approximation holds for :
.
Horizon
On terrestrial planets and other solid celestial bodies with negligible atmospheric effects, the distance to the horizon for a "standard observer" varies as the square root of the planet's radius. Thus, the horizon on Mercury is 62% as far away from the observer as it is on Earth, on Mars the figure is 73%, on the Moon the figure is 52%, on Mimas the figure is 18%, and so on. The observer's height must be taken into account when calculating the distance to the horizon.
Mercury
Because Mercury has little atmosphere, a view of the planet's skies would be no different from viewing space from orbit. Mercury has a southern pole star, α Pictoris, a magnitude 3.2 star. It is fainter than Earth's Polaris (α Ursae Minoris). Omicron Draconis is its north star.
Other planets seen from Mercury
After the Sun, the second-brightest object in the Mercurian sky is Venus, which is much brighter there than for terrestrial observers. The reason for this is that when Venus is closest to Earth, it is between the Earth and the Sun, so we see only its night side. Indeed, even when Venus is brightest in the Earth's sky, we are actually seeing only a narrow crescent. For a Mercurian observer, on the other hand, Venus is closest when it is in opposition to the Sun and is showing its full disk. The apparent magnitude of Venus is as bright as −7.7.
The Earth and the Moon are also very prominent, their apparent magnitudes being about −5 and −1.2, respectively. The maximum apparent distance between the Earth and the Moon is about 15′. All other planets are visible just as they are on Earth, but somewhat less bright at opposition with the difference being most considerable for Mars.
The zodiacal light is probably more prominent than it is from Earth.
Venus
The atmosphere of Venus is so thick that the Sun is not distinguishable in the daytime sky, and the stars are not visible at night. Being closer to the Sun, Venus receives about 1.9 times more sunlight than Earth, but due to the thick atmosphere, only about 20% of the light reaches the surface. Color images taken by the Soviet Venera probes suggest that the sky on Venus is orange. If the Sun could be seen from Venus's surface, the time from one sunrise to the next (a solar day) would be 116.75 Earth days. Because of Venus's retrograde rotation, the Sun would appear to rise in the west and set in the east.
An observer aloft in Venus's cloud tops, on the other hand, would circumnavigate the planet in about four Earth days and see a sky in which Earth and the Moon shine brightly (about magnitudes −6.6 and −2.7, respectively) at opposition. The maximum angular separation between the Moon and Earth from the perspective of Venus is 0.612°, or approximately the same separation of one centimetre of separation at a distance of one metre and coincidentally, about the apparent size of the Moon as seen from Earth. Mercury would also be easy to spot, because it is closer and brighter, at up to magnitude −2.7, and because its maximum elongation from the Sun is considerably larger (40.5°) than when observed from Earth (28.3°).
42 Draconis is the closest star to the north pole of Venus. Eta¹ Doradus is the closest to its south pole. (Note: The IAU uses the right-hand rule to define a positive pole for the purpose of determining orientation. Using this convention, Venus is tilted 177° ("upside down"), and the positive pole is instead the south pole.)
The Moon
The Moon's atmosphere is negligibly thin, essentially vacuum, so its sky is black, as in the case of Mercury. At lunar twilight astronauts have though observed some crepuscular rays and lunar horizon glow of the illuminated atmosphere, beside interplanetary light phenomenons like zodiacal light.
Furthermore, the Sun is so bright that it is still impossible to see stars during the lunar daytime, unless the observer is well shielded from sunlight (direct or reflected from the ground).
The Moon has a southern polar star, δ Doradus, a magnitude 4.34 star. It is better aligned than Earth's Polaris (α Ursae Minoris), but much fainter. Its north pole star is Omicron Draconis.
Sun and Earth in the lunar sky
While the Sun moves across the Moon's sky within fourteen days, the daytime of a lunar day or the lunar month, Earth is only visible on the Moon's near side and moves around a central point in the near side's sky.
This is due to the Moon always facing the Earth with the same side, a result of the Moon's rotation being tidally locked to Earth. That said, the Earth does move around slightly around a central point in the Moon's sky, because of monthly libration.
Therefore rising or setting of Earth at the horizon on the Moon occurs only at few lunar locations and only to a small degree, at the border of the near side of the Moon to the far side, and takes much longer than a sunrise or sunset on Earth due to the Moon's slow monthly rotation.
The famous Earthrise image by Apollo 8 though is an instance where the astronauts moved around the Moon, making the Earth to rise above the Moon because of that motion.
Eclipses from the Moon
When sometimes the Moon, Earth and the Sun align exactly in a straight line (a syzygy), the Moon or Earth move through the other's shadow, producing an eclipse for an observer on the surface in the shadow.
When the Moon moves into Earth's shadow a Solar eclipse occurs on the near side of the Moon (which is observable as a Lunar eclipse facing the Moon).
Since the apparent diameter of the Earth is four times larger than that of the Sun, the Sun would be hidden behind the Earth for hours. Earth's atmosphere would be visible as a reddish ring. During the Apollo 15 mission, an attempt was made to use the Lunar Roving Vehicle's TV camera to view such an eclipse, but the camera or its power source failed after the astronauts left for Earth.
When Earth moves into the Moon's shadow a Solar eclipse occurs on Earth where the Moon's shadow passes, and is visible facing Earth as a tapered out lunar shadow on Earth's surface traveling across the full Earth's disk. The effect would be comparable to the shadow of a golf ball cast by sunlight on an object away. Lunar observers with telescopes might be able to discern the umbral shadow as a black spot at the center of a less dark region (penumbra). It would look essentially the same as it does to the Deep Space Climate Observatory, which orbits Earth at the L1 Lagrangian point in the Sun-Earth system, from Earth.
Mars
Mars has only a thin atmosphere; however, it is extremely dusty and there is much light that is scattered about. The sky is thus rather bright during the daytime and stars are not visible. The Martian northern pole star is Deneb, although the actual pole is somewhat offset in the direction of Alpha Cephei; it is more accurate to state that the top two stars of the Northern Cross, Sadr and Deneb, point to the north Celestial pole of Mars. Kappa Velorum is only a couple of degrees from the south Celestial pole of Mars.
The moons of Mars
Phobos appears in the sky of Mars with an angular size of 4.1, making its shape recognizable, appearing larger than Venus in Earth's sky, while the Moon appears in Earth's sky as large as 31 on average.
The color of the Martian sky
Generating accurate true-color images from Mars' surface is surprisingly complicated. To give but one aspect to consider, there is the Purkinje effect: the human eye's response to color depends on the level of ambient light; red objects appear to darken faster than blue objects as the level of illumination goes down. There is much variation in the color of the sky as reproduced in published images, since many of those images have used filters to maximize their scientific value and are not trying to show true color. For many years, the sky on Mars was thought to be more pinkish than it is now believed to be.
It is now known that during the Martian day, the sky is a butterscotch color. Around sunset and sunrise, the sky is rose in color, but in the vicinity of the setting Sun it is blue. This is the opposite of the situation on Earth. Twilight lasts a long time after the Sun has set and before it rises because of the dust high in Mars's atmosphere.
On Mars, Rayleigh scattering is usually a very weak effect; the red color of the sky is caused by the presence of iron(III) oxide in the airborne dust particles. These particles are larger in size than gas molecules, so most of the light is scattered by Mie scattering. Dust absorbs blue light and scatters longer wavelengths (red, orange, yellow).
The Sun from Mars
The Sun as seen from Mars appears to be the angular diameter as seen from Earth (0.35°), and sends 40% of the light, approximately the brightness of a slightly cloudy afternoon on Earth.
On June 3, 2014, the Curiosity rover on Mars observed the planet Mercury transiting the Sun, marking the first time a planetary transit has been observed from a celestial body besides Earth.
Earth and Moon from Mars
The Earth is visible from Mars as a double star; the Moon would be visible alongside it as a fainter companion. The difference in brightness between the two would be greatest around inferior conjunction. At that time, both bodies would present their dark sides to Mars, but Earth's atmosphere would largely offset this by refracting sunlight much like the atmosphere of Venus does. On the other hand, the airless Moon would behave like the similarly airless Mercury, going completely dark when within a few degrees of the Sun. At inferior conjunction (for the terrestrial observer, this is the opposition of Mars and the Sun), the maximum visible distance between the Earth and the Moon would be about 25′, which is close to the apparent size of the Moon in Earth's sky. The angular size of Earth is between 48.1 and 6.6 and of the Moon between 13.3 and 1.7, comparable to that of Venus and Mercury from Earth. Near maximum elongation (47.4°), the Earth and Moon would shine at apparent magnitudes −2.5 and +0.9, respectively.
Venus from Mars
Venus as seen from Mars (when near the maximum elongation from the Sun of 31.7°) would have an apparent magnitude of about −3.2.
Jupiter
Although no images from within Jupiter's atmosphere have ever been taken, artistic representations typically assume that the planet's sky is blue, though dimmer than Earth's, because the sunlight there is on average 27 times fainter, at least in the upper reaches of the atmosphere. The planet's narrow rings might be faintly visible from latitudes above the equator. Further down into the atmosphere, the Sun would be obscured by clouds and haze of various colors, most commonly blue, brown, and red. Although theories abound on the cause of the colors, there is currently no unambiguous answer.
From Jupiter, the Sun appears to cover only 5 arcminutes, less than a quarter of its size as seen from Earth. The north pole of Jupiter is a little over two degrees away from Zeta Draconis, while its south pole is about two degrees north of Delta Doradus.
Jupiter's moons as seen from Jupiter
Aside from the Sun, the most prominent objects in Jupiter's sky are the four Galilean moons. Io, the nearest to the planet, would be slightly larger than the full moon in Earth's sky, though less bright, and would be the largest moon in the Solar System as seen from its parent planet. The higher albedo of Europa would not overcome its greater distance from Jupiter, so it would not outshine Io. In fact, the low solar constant at Jupiter's distance (3.7% Earth's) ensures that none of the Galilean satellites would be as bright as the full moon is on Earth, and neither would any other moon in the Solar System.
All four Galilean moons stand out because of the swiftness of their motion, compared to the Moon. They are all also large enough to fully eclipse the Sun. Because Jupiter's axial tilt is minimal, and the Galilean moons all orbit in the plane of Jupiter's equator, solar eclipses are quite common.
The skies of Jupiter's moons
None of Jupiter's moons have more than traces of atmosphere, so their skies are very nearly black. For an observer on one of the moons, the most prominent feature of the sky by far would be Jupiter. For an observer on Io, the closest large moon to the planet, Jupiter's apparent diameter would be about 20° (38 times the visible diameter of the Moon, covering 5% of Io's sky). An observer on Metis, the innermost moon, would see Jupiter's apparent diameter increased to 68° (130 times the visible diameter of the Moon, covering 18% of Metis's sky). A "full Jupiter" over Metis shines with about 4% of the Sun's brightness (light on Earth from a full moon is 400,000 times dimmer than sunlight).
Because the inner moons of Jupiter are in synchronous rotation around Jupiter, the planet always appears in nearly the same spot in their skies (Jupiter would wiggle a bit because of the non-zero eccentricities). Observers on the sides of the Galilean satellites facing away from the planet would never see Jupiter, for instance.
From the moons of Jupiter, solar eclipses caused by the Galilean satellites would be spectacular, because an observer would see the circular shadow of the eclipsing moon travel across Jupiter's face.
Saturn
The sky in the upper reaches of Saturn's atmosphere is blue (from imagery of the Cassini mission at the time of its September 2017 demise), but the predominant color of its cloud decks suggests that it may be yellowish further down. Observations from spacecraft show that seasonal smog develops in Saturn's southern hemisphere at its perihelion due to its axial tilt. This could cause the sky to become yellowish at times. As the northern hemisphere is pointed towards the Sun only at aphelion, the sky there would likely remain blue. The rings of Saturn are almost certainly visible from the upper reaches of its atmosphere. The rings are so thin that from a position on Saturn's equator, they would be almost invisible. However, from anywhere else on the planet, they could be seen as a spectacular arc stretching across half the celestial hemisphere.
Delta Octantis is the south pole star of Saturn. Its north pole is in the far northern region of Cepheus, about six degrees from Polaris.
The sky of Titan
Titan is the only moon in the Solar System to have a thick atmosphere. Images from the Huygens probe show that the Titanean sky is a light tangerine color. However, an astronaut standing on the surface of Titan would see a hazy brownish/dark orange color. As a consequence of its greater distance from the Sun and the opacity of its atmosphere, the surface of Titan receives only about of the sunlight Earth does – daytime on Titan is thus only as bright as twilight on the Earth. It seems likely that Saturn is permanently invisible behind orange smog, and even the Sun would be only a lighter patch in the haze, barely illuminating the surface of ice and methane lakes. However, in the upper atmosphere, the sky would have a blue color and Saturn would be visible. With its thick atmosphere and methane rain, Titan is the only celestial body other than Earth upon which rainbows on the surface could form. However, given the extreme opacity of the atmosphere in visible light, the vast majority would be in the infrared.
Uranus
From a vantage above the clouds on Uranus, the sky would probably appear dark blue. It is unlikely that the planet's rings can be seen from the upper atmosphere, as they are very thin and dark. Uranus has a northern polar star, Sabik (η Ophiuchi), a magnitude 2.4 star. Uranus also has a southern polar star, 15 Orionis, a magnitude 4.8 star. Both are fainter than Earth's Polaris (α Ursae Minoris), although Sabik only slightly.
Neptune
The north pole of Neptune points to a spot midway between Gamma and Delta Cygni. Its south pole star is Gamma Velorum.
Judging by the color of its atmosphere, the sky of Neptune is probably an azure or sky blue, similar to Uranus's. As in the case of Uranus, it is unlikely that the planet's rings can be seen from the upper atmosphere, as they are very thin and dark.
Aside from the Sun, the most notable object in Neptune's sky is its large moon Triton, which would appear slightly smaller than a full Moon on Earth. It moves more swiftly than the Moon, because of its shorter period (5.8 days) compounded by its retrograde orbit. The smaller moon Proteus would show a disk about half the size of the full Moon. Surprisingly, Neptune's small inner moons all cover, at some point in their orbits, more than 10′ in Neptune's sky. At some points, Despina's angular diameter rivals that of Ariel from Uranus and Ganymede from Jupiter. Here are the angular diameters for Neptune's moons (for comparison, Earth's moon measures on average 31′ for terrestrial observers): Naiad, 7–13′; Thalassa, 8–14′; Despina, 14–22′; Galatea, 13–18′; Larissa, 10–14′; Proteus, 12–16′; Triton, 26–28′. An alignment of the inner moons would likely produce a spectacular sight. Neptune's largest outer satellite, Nereid, is not large enough to appear as a disk from Neptune, and is not noticeable in the sky, as its brightness at full phase varies from magnitude 2.2–6.4, depending on which point in its eccentric orbit it happens to be. The other irregular outer moons would not be visible to the naked eye, although a dedicated telescopic observer could potentially spot some at full phase.
As with Uranus, the low light levels cause the major moons to appear very dim. The brightness of Triton at full phase is only −7.11, despite the fact that Triton is more than four times as intrinsically bright as Earth's moon and orbits much closer to Neptune.
The sky of Triton
Triton, Neptune's largest moon, has a hazy atmosphere composed primarily of nitrogen. Because Triton orbits with synchronous rotation, Neptune always appears in the same position in its sky. Triton's rotation axis is inclined 130° to Neptune's orbital plane and thus points within 40° of the Sun twice per Neptunian year, much like Uranus's. As Neptune orbits the Sun, Triton's polar regions take turns facing the Sun for 82 years at a stretch, resulting in radical seasonal changes as one pole, then the other, moves into the sunlight.
Neptune itself would span 8 degrees in Triton's sky, though with a maximum brightness roughly comparable to that of the full moon on Earth it would appear only about as bright as the full moon, per unit area. Due to its eccentric orbit, Nereid would vary considerably in brightness, from fifth to first magnitude; its disk would be far too small to see with the naked eye. Proteus would also be difficult to resolve at just 5–6 arcminutes across, but it would never be fainter than first magnitude, and at its closest would rival Canopus.
Trans-Neptunian objects
A trans-Neptunian object is any minor planet in the Solar System that orbits the Sun at a greater average distance (semi-major axis) than Neptune, 30 astronomical units (AU).
Pluto and Charon
Pluto, accompanied by its largest moon Charon, orbits the Sun at a distance usually outside the orbit of Neptune except for a twenty-year period in each orbit.
From Pluto, the Sun is point-like to human eyes, but still very bright, giving roughly 150 to 450 times the light of the full Moon from Earth (the variability being due to the fact that Pluto's orbit is highly elliptical, stretching from just 4.4 billion km to over 7.3 billion km from the Sun). Nonetheless, human observers would notice a large decrease in available light: the solar illuminance at Pluto's average distance is about 85 lx, which is equivalent to the lighting of an office building's hallway or restroom.
Pluto's atmosphere consists of a thin envelope of nitrogen, methane, and carbon monoxide gases, all of which are derived from the ices of these substances on its surface. When Pluto is close to the Sun, the temperature of Pluto's solid surface increases, causing these ices to sublimate into gases. This atmosphere also produces a noticeable blue haze that is visible at sunset and possibly other times of the Plutonian day.
Pluto and Charon are tidally locked to each other. This means that Charon always presents the same face to Pluto, and Pluto also always presents the same face to Charon. Observers on the far side of Charon from Pluto would never see the dwarf planet; observers on the far side of Pluto from Charon would never see the moon. Every 124 years, for several years it is mutual-eclipse season, during which Pluto and Charon each alternately eclipse the Sun for the other at intervals of 3.2 days. Charon, as seen from Pluto's surface at the sub-Charon point, has an angular diameter of about 3.8°, nearly eight times the Moon's angular diameter as seen from Earth and about 56 times the area. It would be a very large object in the night sky, shining about 8% as bright as the Moon (it would appear darker than the Moon because its lesser illumination comes from a larger disc). Charon's illuminance would be about 14 mlx (for comparison, a moonless clear night sky is 2 mlx while a full Moon is between 300 and 50 mlx).
Extrasolar planets
For observers on extrasolar planets, the constellations would differ depending on the distances involved. The view of outer space of exoplanets can be extrapolated from open source software such as Celestia or Stellarium. Due to parallax, distant stars change their position less than nearby ones. For alien observers, the Sun would be visible to the naked human eye only at distances below 20 – 27 parsec (60–90 ly). If the Sun were to be observed from another star, it would always appear on the opposite coordinates in the sky. Thus, an observer located near a star with RA at 4 hr and declination −10 would see the Sun located at RA: 16 hr, dec: +10. A consequence of observing the universe from other stars is that stars that may appear bright in our own sky may appear dimmer in other skies and vice versa.
In May 2017, glints of light from Earth, seen as twinkling by DSCOVR, a satellite stationed roughly a million miles from Earth at the Earth-Sun L1 Lagrange point, were found to be reflected light from ice crystals in the atmosphere. The technology used to determine this may be useful in studying the atmospheres of distant worlds, including those of exoplanets.
The position of stars in extrasolar skies differs the least to the positions in Earth's sky at the closest stars to Earth, with nearby stars shifting position the most.
The Sun would appear as a bright star only at the closest stars. At the Alpha Centauri star system the Sun would appear as a bright star continuing the wavy line of Cassiopeia eastward, while Sirius would shift to a position just next to Betelgeuse and its own Proxima Centauri red dwarf would still appear as a dim star contrary to its main A and B stars. At Barnard's star the Sun would appear between the not much shifted Sirius and Belt of Orion compared to in the sky of Earth. Conversely the Sun would appear from Sirius and also Procyon around Altair.
Planets of the TRAPPIST-1 system orbit extremely close together, enough so that each planet of the system would provide a detailed view of the other six. Planets of the TRAPPIST-1 system would appear in the sky with angular diameters comparable to the moon as viewed from Earth. Under clear viewing conditions, details such as phases and surface features would be easily visible to the naked eye.
From the Large Magellanic Cloud
From a viewpoint in the LMC, the Milky Way's total apparent magnitude would be −2.0—over 14 times brighter than the LMC appears to us on Earth—and it would span about 36° across the sky, the width of over 70 full moons. Furthermore, because of the LMC's high galactic latitude, an observer there would get an oblique view of the entire galaxy, free from the interference of interstellar dust that makes studying in the Milky Way's plane difficult from Earth. The Small Magellanic Cloud would be about magnitude 0.6, substantially brighter than the LMC appears to us.
See also
Exosphere
Pole star § Other planets
Sky
Timeline of first images of Earth from space
Notes
References
Further reading
External links
Astronauts on the planets
Essay on the possible sky colours of alien worlds.
JPL Solar System Simulator
Phases of Charon as seen from Pluto
The Starry Universe – Life magazine (December 20, 1954).
Sunsets simulated on other planets (NASA; June 22, 2020)
Observational astronomy
Planetary science | Extraterrestrial sky | [
"Astronomy"
] | 5,935 | [
"Planetary science",
"Observational astronomy",
"Astronomical sub-disciplines"
] |
602,845 | https://en.wikipedia.org/wiki/Petrifaction | In geology, petrifaction or petrification () is the process by which organic material becomes a fossil through the replacement of the original material and the filling of the original pore spaces with minerals. Petrified wood typifies this process, but all organisms, from bacteria to vertebrates, can become petrified (although harder, more durable matter such as bone, beaks, and shells survive the process better than softer remains such as muscle tissue, feathers, or skin). Petrification takes place through a combination of two similar processes: permineralization and replacement. These processes create replicas of the original specimen that are similar down to the microscopic level.
Processes
Permineralization
One of the processes involved in petrifaction is permineralization. The fossils created through this process tend to contain a large amount of the original material of the specimen. This process occurs when groundwater containing dissolved minerals (most commonly quartz, calcite, apatite (calcium phosphate), siderite (iron carbonate), and pyrite), fills pore spaces and cavities of specimens, particularly bone, shell or wood. The pores of the organisms' tissues are filled when these minerals precipitate out of the water. Two common types of permineralization are silicification and pyritization.
Silicification
Silicification is the process in which organic matter becomes saturated with silica. A common source of silica is volcanic material. Studies have shown that in this process, most of the original organic matter is destroyed. Silicification most often occurs in two environments—either the specimen is buried in sediments of deltas and floodplains or organisms are buried in volcanic ash. Water must be present for silicification to occur because it reduces the amount of oxygen present and therefore reduces the deterioration of the organism by fungi, maintains organism shape, and allows for the transportation and deposition of silica. The process begins when a specimen is permeated with an aqueous silica solution. The cell walls of the specimen are progressively dissolved and silica is deposited into the empty spaces. In wood samples, as the process proceeds, cellulose and lignin, two components of wood, are degraded and replaced with silica. The specimen is transformed to stone (a process called lithification) as water is lost. For silicification to occur, the geothermic conditions must include a neutral to slightly acidic pH and a temperature and pressure similar to shallow-depth sedimentary environments. Under ideal natural conditions, silicification can occur at rates approaching those seen in artificial petrification.
Pyritization
Pyritization is a process similar to silicification, but instead involves the deposition of iron and sulfur in the pores and cavities of an organism. Pyritization can result in both solid fossils as well as preserved soft tissues. In marine environments, pyritization occurs when organisms are buried in sediments containing a high concentration of iron sulfides. Organisms release sulfide, which reacts with dissolved iron in the surrounding water, when they decay. This reaction between iron and sulfides forms pyrite (FeS2). Carbonate shell material of the organism is then replaced with pyrite due to a higher concentration of pyrite and a lower concentration of carbonate in the surrounding water. Pyritization occurs to a lesser extent in plants in clay environments.
Replacement
Replacement, the second process involved in petrifaction, occurs when water containing dissolved minerals dissolves the original solid material of an organism, which is then replaced by minerals. This can take place extremely slowly, replicating the microscopic structure of the organism. The slower the rate of the process, the better defined the microscopic structure will be. The minerals commonly involved in replacement are calcite, silica, pyrite, and hematite. Biotic remains preserved by replacement alone (as opposed to in combination with permineralization) are rarely found, but these fossils present significance to paleontology because they tend to be more detailed.
Uses
Not only are the fossils produced through the process of petrifaction used for paleontological study, but they have also been used as both decorative and informative pieces. Petrified wood is used in several ways. Slabs of petrified wood can be crafted into tabletops, or the slabs themselves are sometimes displayed in a decorative fashion. Also, larger pieces of the wood have been carved into sinks and basins. Other large pieces can also be crafted into chairs and stools. Petrified wood and other petrified organisms have also been used in jewelry, sculpture, clock-making, ashtrays and fruit bowls, and landscape and garden decorations.
Architecture
Petrified wood has also been used in construction. The Petrified Wood Gas Station, located on Main St Lamar, Colorado, was built in 1932 and consists of walls and floors constructed from pieces of petrified wood. The structure, built by W.G. Brown, has since been converted to office space and a used car dealership. Glen Rose, Texas provides even more examples of the use of fossilized wood in architecture. Beginning in the 1920s, the farmers of Somervell County, Texas began uncovering petrified trees. Local craftsmen and masons then built over 65 structures from this petrified wood, 45 of which were still standing as of June 2009. These structures include gas stations, flowerbeds, cottages, restaurants, fountains and gateposts. Glen Rose, Texas is also noted for Dinosaur Valley State Park and the Glen Rose Formation, where fossilized dinosaur footprints from the Cretaceous period can be viewed. Another example of the use of petrified wood in construction is the Agate House Pueblo in the Petrified Forest National Park in Arizona. Built by ancestral Pueblo people about 990 years ago, this eight-room building was constructed almost entirely out of petrified wood and is believed to have served as either a family home or meeting place.
Artificial petrifaction
Scientists attempted to artificially petrify organisms as early as the 18th century, when Girolamo Segato claimed to have supposedly "petrified" human remains. His methods were lost, but the bulk of his "pieces" are on display at the Museum of the Department of Anatomy in Florence, Italy.
More recent attempts have been both successful and documented, but should be considered as semi-petrifaction or incomplete petrifaction or at least as producing some novel type of wood composite, as the wood material remains to a certain degree; the constituents of wood (cellulose, lignins, lignans, oleoresins, etc.) have not been replaced by silicate, but have been infiltrated by specially formulated acidic solutions of aluminosilicate salts that gel in contact with wood matter and form a matrix of silicates within the wood after being left to react slowly for a given period of time in the solution or heat-cured for faster results. Hamilton Hicks of Greenwich, Connecticut, received a patent for his "recipe" for rapid artificial petrifaction of wood under US patent 4,612,050 in 1986. Hicks' recipe consists of highly mineralized water and a sodium silicate solution combined with a dilute acid with a pH of 4.0-5.5. Samples of wood are penetrated with this mineral solution through repeated submersion and applications of the solution. Wood treated in this fashion is - according to the claims in the patent - incapable of being burned and acquires the features of petrified wood. Some uses of this product as suggested by Hicks include use by horse breeders who desire fireproof stables constructed of nontoxic material that would also be resistant to chewing of the wood by horses.
In 2005 scientists at the Pacific Northwest National Laboratory (PNNL) reported that they had successfully petrified wood samples artificially. Unlike natural petrification, though, they infiltrated samples in acidic solutions, diffused them internally with titanium and carbon and fired them in a high-temperature oven (circa 1400 °C) in an inert atmosphere to yield a man-made ceramic matrix composite of titanium carbide and silicon carbide still showing the initial structure of wood. Future uses could see these artificially petrified wood-ceramic materials eventually used in the tool industry. Other vegetal matter could be treated in a similar process and yield abrasive powders.
See also
Girolamo Segato
References
Botany
Fossilization
Sedimentary rocks | Petrifaction | [
"Biology"
] | 1,734 | [
"Plants",
"Botany"
] |
16,153,022 | https://en.wikipedia.org/wiki/Expanded%20genetic%20code | An expanded genetic code is an artificially modified genetic code in which one or more specific codons have been re-allocated to encode an amino acid that is not among the 22 common naturally-encoded proteinogenic amino acids.
The key prerequisites to expand the genetic code are:
the non-standard amino acid to encode,
an unused codon to adopt,
a tRNA that recognizes this codon, and
a tRNA synthetase that recognizes only that tRNA and only the non-standard amino acid.
Expanding the genetic code is an area of research of synthetic biology, an applied biological discipline whose goal is to engineer living systems for useful purposes. The genetic code expansion enriches the repertoire of useful tools available to science.
In May 2019, researchers, in a milestone effort, reported the creation of a new synthetic (possibly artificial) form of viable life, a variant of the bacteria Escherichia coli, by reducing the natural number of 64 codons in the bacterial genome to 61 codons (eliminating two out of the six codons coding for serine and one out of three stop codons) – of which 59 used to encode 20 amino acids.
Introduction
It is noteworthy that the genetic code for all organisms is basically the same, so that all living beings use the same 'genetic language'. In general, the introduction of new functional unnatural amino acids into proteins of living cells breaks the universality of the genetic language, which ideally leads to alternative life forms. Proteins are produced thanks to the translational system molecules, which decode the RNA messages into a string of amino acids. The translation of genetic information contained in messenger RNA (mRNA) into a protein is catalysed by ribosomes. Transfer RNAs (tRNA) are used as keys to decode the mRNA into its encoded polypeptide. The tRNA recognizes a specific three nucleotide codon in the mRNA with a complementary sequence called the anticodon on one of its loops. Each three-nucleotide codon is translated into one of twenty naturally occurring amino acids. There is at least one tRNA for any codon, and sometimes multiple codons code for the same amino acid. Many tRNAs are compatible with several codons. An enzyme called an aminoacyl tRNA synthetase covalently attaches the amino acid to the appropriate tRNA. Most cells have a different synthetase for each amino acid (20 or more synthetases). On the other hand, some bacteria have fewer than 20 aminoacyl tRNA synthetases, and introduce the "missing" amino acid(s) by modification of a structurally related amino acid by an aminotransferase enzyme. A feature exploited in the expansion of the genetic code is the fact that the aminoacyl tRNA synthetase often does not recognize the anticodon, but another part of the tRNA, meaning that if the anticodon were to be mutated the encoding of that amino acid would change to a new codon. In the ribosome, the information in mRNA is translated into a specific amino acid when the mRNA codon matches with the complementary anticodon of a tRNA, and the attached amino acid is added onto a growing polypeptide chain. When it is released from the ribosome, the polypeptide chain folds into a functioning protein.
In order to incorporate a novel amino acid into the genetic code several changes are required. First, for successful translation of a novel amino acid, the codon to which the novel amino acid is assigned cannot already code for one of the 20 natural amino acids. Usually a nonsense codon (stop codon) or a four-base codon are used. Second, a novel pair of tRNA and aminoacyl tRNA synthetase are required, these are called the orthogonal set. The orthogonal set must not crosstalk with the endogenous tRNA and synthetase sets, while still being functionally compatible with the ribosome and other components of the translation apparatus. The active site of the synthetase is modified to accept only the novel amino acid. Most often, a library of mutant synthetases is screened for one which charges the tRNA with the desired amino acid. The synthetase is also modified to recognize only the orthogonal tRNA. The tRNA synthetase pair is often engineered in other bacteria or eukaryotic cells.
In this area of research, the 20 encoded proteinogenic amino acids are referred to as standard amino acids, or alternatively as natural or canonical amino acids, while the added amino acids are called non-standard amino acids (NSAAs), or unnatural amino acids (uAAs; term not used in papers dealing with natural non-proteinogenic amino acids, such as phosphoserine), or non-canonical amino acids.
Non-standard amino acids
The first element of the system is the amino acid that is added to the genetic code of a certain strain of organism.
Over 71 different NSAAs have been added to different strains of E. coli, yeast or mammalian cells. Due to technical details (easier chemical synthesis of NSAAs, less crosstalk and easier evolution of the aminoacyl-tRNA synthase), the NSAAs are generally larger than standard amino acids and most often have a phenylalanine core but with a large variety of different substituents. These allow a large repertoire of new functions, such as labeling (see figure), as a fluorescent reporter (e.g. dansylalanine) or to produce translational proteins in E. coli with Eukaryotic post-translational modifications (e.g. phosphoserine, phosphothreonine, and phosphotyrosine).
The founding work was reported by Rolf Furter, who singlehandedly used yeast tRNAPhe/PheRS pair to incorporate p-iodophenylalanine in E. coli.
Unnatural amino acids incorporated into proteins include heavy atom-containing amino acids to facilitate certain x-ray crystallographic studies; amino acids with novel steric/packing and electronic properties; photocrosslinking amino acids which can be used to probe protein-protein interactions in vitro or in vivo; keto, acetylene, azide, and boronate-containing amino acids which can be used to selectively introduce a large number of biophysical probes, tags, and novel chemical functional groups into proteins in vitro or in vivo; redox active amino acids to probe and modulate electron transfer; photocaged and photoisomerizable amino acids to photoregulate biological processes; metal binding amino acids for catalysis and metal ion sensing; amino acids that contain fluorescent or infra-red active side chains to probe protein structure and dynamics; α-hydroxy acids and D-amino acids as probes of backbone conformation and hydrogen bonding interactions; and sulfated amino acids and mimetics of phosphorylated amino acids as probes of post-translational modifications.
Availability of the non-standard amino acid requires that the organism either import it from the medium or biosynthesize it. In the first case, the unnatural amino acid is first synthesized chemically in its optically pure L-form. It is then added to the growth medium of the cell. A library of compounds is usually tested for use in incorporation of the new amino acid, but this is not always necessary, for example, various transport systems can handle unnatural amino acids with apolar side-chains. In the second case, a biosynthetic pathway needs to be engineered, for example, an E. coli strain that biosynthesizes a novel amino acid (p-aminophenylalanine) from basic carbon sources and includes it in its genetic code. Another example: the production of phosphoserine, a natural metabolite, and consequently required alteration of its pathway flux to increase its production.
Codon assignment
Another element of the system is a codon to allocate to the new amino acid.
A major problem for the genetic code expansion is that there are no free codons. The genetic code has a non-random layout that shows tell-tale signs of various phases of primordial evolution, however, it has since frozen into place and is near-universally conserved. Nevertheless, some codons are rarer than others. In fact, in E. coli (and all organisms) the codon usage is not equal, but presents several rare codons (see table), the rarest being the amber stop codon (UAG).
Amber codon suppression
The possibility of reassigning codons was realized by Normanly et al. in 1990, when a viable mutant strain of E. coli read through the UAG ("amber") stop codon.
This was possible thanks to the rarity of this codon and the fact that release factor 1 alone makes the amber codon terminate translation. Later, in the Schultz lab, the tRNATyr/tyrosyl-tRNA synthetase (TyrRS) from Methanococcus jannaschii, an archaebacterium, was used to introduce a tyrosine instead of STOP, the default value of the amber codon. This was possible because of the differences between the endogenous bacterial syntheses and the orthologous archaeal synthase, which do not recognize each other. Subsequently, the group evolved the orthologonal tRNA/synthase pair to utilize the non-standard amino acid O-methyltyrosine. This was followed by the larger naphthylalanine and the photocrosslinking benzoylphenylalanine, which proved the potential utility of the system.
The amber codon is the least used codon in Escherichia coli, but hijacking it results in a substantial loss of fitness. One study, in fact, found that there were at least 83 peptides majorly affected by the readthrough Additionally, the labelling was incomplete. As a consequence, several strains have been made to reduce the fitness cost, including the removal of all amber codons from the genome. In most E. coli K-12 strains (viz. Escherichia coli (molecular biology) for strain pedigrees) there are 314 UAG stop codons. Consequently, a gargantuan amount of work has gone into the replacement of these. One approach pioneered by the group of Prof. George Church from Harvard, was dubbed MAGE in CAGE: this relied on a multiplex transformation and subsequent strain recombination to remove all UAG codons—the latter part presented a halting point in a first paper, but was overcome. This resulted in the E. coli strain C321.ΔA, which lacks all UAG codons and RF1. This allowed an experiment to be done with this strain to make it "addicted" to the amino acid biphenylalanine by evolving several key enzymes to require it structurally, therefore putting its expanded genetic code under positive selection.
Rare sense codon reassignment
In addition to the amber codon, rare sense codons have also been considered for use. The AGG codon codes for arginine, but a strain has been successfully modified to make it code for 6-N-allyloxycarbonyl-lysine.
Another candidate is the AUA codon, which is unusual in that its respective tRNA has to differentiate against AUG that codes for methionine (primordially, isoleucine, hence its location). In order to do this, the AUA tRNA has a special base, lysidine. The deletion of the synthase (tilS) was possible thanks to the replacement of the native tRNA with that of Mycoplasma mobile (no lysidine). The reduced fitness is a first step towards pressuring the strain to lose all instances of AUA, allowing it to be used for genetic code expansion.
E. coli strain Syn61 is a variant where all uses of TCG (Ser), TCA (Ser), TAG (STOP) codons are eliminated using a synthetic genome (see below). By removing the unneeded tRNA genes and RF1, strain Syn61Δ3 was produced. The three freed codons then become available for adding three special residues, as demonstrated in strain "Syn61Δ3(ev4)".
Four base (quadruplet) codons
While triplet codons are the basis of the genetic code in nature, programmed +1 frameshift is a natural process that allows the use of a four-nucleotide sequence (quadruplet codon) to encode an amino acid. Recent developments in genetic code engineering also showed that quadruplet codon could be used to encode non-standard amino acids under experimental conditions. This allowed the simultaneous usage of two unnatural amino acids, p-azidophenylalanine (pAzF) and N6-[(2-propynyloxy)carbonyl]lysine (CAK), which cross-link with each other by Huisgen cycloaddition. Quadrupled decoding in wild-type, non-recoded strains is very inefficient. This stems from the fact that the interaction between engineered tRNAs with ternary complexes or other translation components is not as favorable and strong as with cell endogenous translation elements. This problem can be overcome by specifically engineering and evolving tRNA that can decode quadruplet codons in non-recoded strains. Up to 4 different quadruplet orthogonal tRNA/tRNA synthethase pairs can be generated in this manner. Quadruplet codon decoding approach has also been applied to the construction of an HIV-1 vaccine.
tRNA/synthetase pair
Another key element is the tRNA/synthetase pair.
The orthologous set of synthetase and tRNA can be mutated and screened through directed evolution to charge the tRNA with a different, even novel, amino acid. Mutations to the plasmid containing the pair can be introduced by error-prone PCR or through degenerate primers for the synthetase's active site. Selection involves multiple rounds of a two-step process, where the plasmid is transferred into cells expressing chloramphenicol acetyl transferase with a premature amber codon. In the presence of toxic chloramphenicol and the non-natural amino acid, the surviving cells will have overridden the amber codon using the orthogonal tRNA aminoacylated with either the standard amino acids or the non-natural one. To remove the former, the plasmid is inserted into cells with a barnase gene (toxic) with a premature amber codon but without the non-natural amino acid, removing all the orthogonal syntheses that do not specifically recognize the non-natural amino acid.
In addition to the recoding of the tRNA to a different codon, they can be mutated to recognize a four-base codon, allowing additional free coding options.
The non-natural amino acid, as a result, introduces diverse physicochemical and biological properties in order to be used as a tool to explore protein structure and function or to create novel or enhanced protein for practical purposes.
Orthogonal sets in model organisms
The orthogonal pairs of synthetase and tRNA that work for one organism may not work for another, as the synthetase may mis-aminoacylate endogenous tRNAs or the tRNA be mis-aminoacylated itself by an endogenous synthetase. As a result, the sets created to date differ between organisms.
In 2017, a mouse engineered with an extended genetic code that can produce proteins with unnatural amino acids was reported.
Orthogonal ribosomes
Similarly to orthogonal tRNAs and aminoacyl tRNA synthetases (aaRSs), orthogonal ribosomes have been engineered to work in parallel to the natural ribosomes. Orthogonal ribosomes ideally use different mRNA transcripts than their natural counterparts and ultimately should draw on a separate pool of tRNA as well. This should alleviate some of the loss of fitness which currently still arises from techniques such as Amber codon suppression. Additionally, orthogonal ribosomes can be mutated and optimized for particular tasks, like the recognition of quadruplet codons. Such an optimization is not possible, or highly disadvantageous for natural ribosomes.
o-Ribosome
In 2005, three sets of ribosomes were published, which did not recognize natural mRNA, but instead translated a separate pool of orthogonal mRNA (o-mRNA). This was achieved by changing the recognition sequence of the mRNA, the Shine-Dalgarno sequence, and the corresponding recognition sequence in the 16S rRNA of ribosomes, the so-called Anti-Shine-Dalgarno-Sequence. This way the base pairing, which is usually lost if either sequence is mutated, stays available. However the mutations in the 16S rRNA were not limited to the obviously base-pairing nucleotides of the classical Anti-Shine-Dalgarno sequence.
Ribo-X
In 2007, the group of Jason W. Chin presented an orthogonal ribosome, which was optimized for Amber codon suppression. The 16S rRNA was mutated in such a way that it bound the release factor RF1 less strongly than the natural ribosome does. This ribosome did not eliminate the problem of lowered cell fitness caused by suppressed stop codons in natural proteins. However through the improved specificity it raised the yields of correctly synthesized target protein significantly (from ~20% to >60% percent for one amber codon to be suppressed and from <1% to >20% for two amber codons).
Ribo-Q
In 2010, the group of Jason W. Chin presented a further optimized version of the orthogonal ribosome. The Ribo-Q is a 16S rRNA optimized to recognize tRNAs, which have quadruplet anti-codons to recognize quadruplet codons, instead of the natural triplet codons. With this approach the number of possible codons rises from 64 to 256. Even accounting for a variety of stop codons, more than 200 different amino acids could potentially be encoded this way.
Ribosome stapling
The orthogonal ribosomes described above all focus on optimizing the 16S rRNA. Thus far, this optimized 16S rRNA was combined with natural large-subunits to form orthogonal ribosomes. If the 23S rRNA, the main RNA-component of the large ribosomal subunit, is to be optimized as well, it had to be assured, that there was no crosstalk in the assembly of orthogonal and natural ribosomes (see figureX B). To ensure that optimized 23S rRNA would only form into ribosomes with the optimized 16S rRNA, the two rRNAs were combined into one transcript. By inserting the sequence for the 23S rRNA into a loop-region of the 16S rRNA sequence, both subunits still adopt functioning folds. Since the two rRNAs are linked and thus in constant proximity, they preferably bind each other, not other free floating ribosomal subunits.
Engineered peptidyl transferase center
In 2014, it was shown that by altering the peptidyl transferase center of the 23S rRNA, ribosomes could be created which draw on orthogonal pools of tRNA. The 3' end of tRNAs is universally conserved to be CCA. The two cytidines base pair with two guanines the 23S rRNA to bind the tRNA to the ribosome. This interaction is required for translational fidelity. However, by co-mutating the binding nucleotides in such a way, that they can still base pair, the translational fidelity can be conserved. The 3'-end of the tRNA is mutated from CCA to CGA, while two cytidine nucleotides in the ribosomes A- and P-sites are mutated to guanidine. This leads to ribosomes which do not accept naturally occurring tRNAs as substrates and to tRNAs, which cannot be used as substrate by natural ribosomes.
To use such tRNAs effectively, they would have to be aminoacylated by specific, orthogonal aaRSs. Most naturally occurring aaRSs recognize the 3'-end of their corresponding tRNA. aaRSs for these 3'-mutated tRNAs are not available yet. Thus far, this system has only been shown to work in an in-vitro translation setting where the aminoacylation of the orthogonal tRNA was achieved using so called "flexizymes". Flexizymes are ribozymes with tRNA-amino-aclylation activity.
Applications
With an expanded genetic code, the unnatural amino acid can be genetically directed to any chosen site in the protein of interest. The high efficiency and fidelity of this process allows a better control of the placement of the modification compared to modifying the protein post-translationally, which, in general, will target all amino acids of the same type, such as the thiol group of cysteine and the amino group of lysine. Also, an expanded genetic code allows modifications to be carried out in vivo.
The ability to site-specifically direct lab-synthesized chemical moieties into proteins allows many types of studies that would otherwise be extremely difficult, such as:
Probing protein structure and function: By using amino acids with slightly different size such as O-methyltyrosine or dansylalanine instead of tyrosine, and by inserting genetically coded reporter moieties (color-changing and/or spin-active) into selected protein sites, chemical information about the protein's structure and function can be measured.
Probing the role of post-translational modifications in protein structure and function: By using amino acids that mimic post-translational modifications such as phosphoserine, biologically active protein can be obtained, and the site-specific nature of the amino acid incorporation can lead to information on how the position, density, and distribution of protein phosphorylation effect protein function.
Identifying and regulating protein activity: By using photocaged aminoacids, protein function can be "switched" on or off by illuminating the organism.
Changing the mode of action of a protein: One can start with the gene for a protein that binds a certain sequence of DNA and, by inserting a chemically active amino acid into the binding site, convert it to a protein that cuts the DNA rather than binding it.
Improving immunogenicity and overcoming self-tolerance: By replacing strategically chosen tyrosines with p-nitro phenylalanine, a tolerated self-protein can be made immunogenic.
Selective destruction of selected cellular components: using an expanded genetic code, unnatural, destructive chemical moieties (sometimes called "chemical warheads") can be incorporated into proteins that target specific cellular components.
Producing better protein: the evolution of T7 bacteriophages on a non-evolving E. coli strain that encoded 3-iodotyrosine on the amber codon, resulted in a population fitter than wild-type thanks to the presence of iodotyrosine in its proteome
Probing protein localization and protein-protein interaction in bacteria.
Future
The expansion of the genetic code is still in its infancy. Current methodology uses only one non-standard amino acid at the time, whereas ideally multiple could be used. In fact, the group of Jason Chin has recently broken the record for a genetically recoded E. coli strain that can simultaneously incorporate up to 4 unnatural amino acids. Moreover, there has been development in software that allows combination of orthogonal ribosomes and unnatural tRNA/RS pairs in order to improve protein yield and fidelity.
Recoded synthetic genome
One way to achieve the encoding of multiple unnatural amino acids is by synthesising a rewritten genome. In 2010, at the cost of $40 million an organism, Mycoplasma laboratorium, was constructed that was controlled by a synthetic, but not recoded, genome. The first genetically recoded organism was created by a collaboration between George Church's and Farren Isaacs' labs, when the wild type was recoded in such a way that all 321 known UAG stop codons were substituted with synonymous UAA codons and release factor 1 was knocked out in order to eliminate the interaction with the exogenous stop codon and improve unnatural protein synthesis. In 2019, Escherichia coli Syn61 was created, with a 4 megabase recoded genome consisting of only 61 codons instead of the natural 64.
In addition to the elimination of the usage of rare codons, the specificity of the system needs to be increased as many tRNA recognise several codons
Expanded genetic alphabet
Another approach is to expand the number of nucleobases to increase the coding capacity.
An unnatural base pair (UBP) is a designed subunit (or nucleobase) of DNA which is created in a laboratory and does not occur in nature. A demonstration of UBPs were achieved in vitro by Ichiro Hirao's group at RIKEN institute in Japan. In 2002, they developed an unnatural base pair between 2-amino-8-(2-thienyl)purine (s) and pyridine-2-one (y) that functions in vitro in transcription and translation for the site-specific incorporation of non-standard amino acids into proteins. In 2006, they created 7-(2-thienyl)imidazo[4,5-b]pyridine (Ds) and pyrrole-2-carbaldehyde (Pa) as a third base pair for replication and transcription. Afterward, Ds and 4-[3-(6-aminohexanamido)-1-propynyl]-2-nitropyrrole (Px) was discovered as a high fidelity pair in PCR amplification. In 2013, they applied the Ds-Px pair to DNA aptamer generation by in vitro selection (SELEX) and demonstrated the genetic alphabet expansion significantly augment DNA aptamer affinities to target proteins.
In 2012, a group of American scientists led by Floyd Romesberg, a chemical biologist at the Scripps Research Institute in San Diego, California, published that his team designed an unnatural base pair (UBP). The two new artificial nucleotides or Unnatural Base Pair (UBP) were named "d5SICS" and "dNaM." More technically, these artificial nucleotides bearing hydrophobic nucleobases, feature two fused aromatic rings that form a (d5SICS–dNaM) complex or base pair in DNA. In 2014 the same team from the Scripps Research Institute reported that they synthesized a stretch of circular DNA known as a plasmid containing natural T-A and C-G base pairs along with the best-performing UBP Romesberg's laboratory had designed, and inserted it into cells of the common bacterium E. coli that successfully replicated the unnatural base pairs through multiple generations. This is the first known example of a living organism passing along an expanded genetic code to subsequent generations. This was in part achieved by the addition of a supportive algal gene that expresses a nucleotide triphosphate transporter which efficiently imports the triphosphates of both d5SICSTP and dNaMTP into E. coli bacteria. Then, the natural bacterial replication pathways use them to accurately replicate the plasmid containing d5SICS–dNaM.
The successful incorporation of a third base pair into a living micro-organism is a significant breakthrough toward the goal of greatly expanding the number of amino acids which can be encoded by DNA, thereby expanding the potential for living organisms to produce novel proteins. The artificial strings of DNA do not encode for anything yet, but scientists speculate they could be designed to manufacture new proteins which could have industrial or pharmaceutical uses.
In May 2014, researchers announced that they had successfully introduced two new artificial nucleotides into bacterial DNA, and by including individual artificial nucleotides in the culture media, were able to induce amplification of the plasmids containing the artificial nucleotides by a factor of 2 x 107 (24 doublings); they did not create mRNA or proteins able to use the artificial nucleotides.
Related methods
Selective pressure incorporation (SPI) method for production of alloproteins
There have been many studies that have produced protein with non-standard amino acids, but they do not alter the genetic code. These protein, called alloprotein, are made by incubating cells with an unnatural amino acid in the absence of a similar coded amino acid in order for the former to be incorporated into protein in place of the latter, for example L-2-aminohexanoic acid (Ahx) for methionine (Met).
These studies rely on the natural promiscuous activity of the aminoacyl tRNA synthetase to add to its target tRNA an unnatural amino acid (i.e. analog) similar to the natural substrate, for example methionyl-tRNA synthase's mistaking isoleucine for methionine. In protein crystallography, for example, the addition of selenomethionine to the media of a culture of a methionine-auxotrophic strain results in proteins containing selenomethionine as opposed to methionine (viz. Multi-wavelength anomalous dispersion for reason). Another example is that photoleucine and photomethionine are added instead of leucine and methionine to cross-label protein.
Similarly, some tellurium-tolerant fungi can incorporate tellurocysteine and telluromethionine into their protein instead of cysteine and methionine.
The objective of expanding the genetic code is more radical as it does not replace an amino acid, but it adds one or more to the code. On the other hand, proteome-wide replacements are most efficiently performed by global amino acid substitutions. For example, global proteome-wide substitutions of natural amino acids with fluorinated analogs have been attempted in E. coli and B. subtilis. A complete tryptophan substitution with thienopyrrole-alanine in response to 20899 UGG codons in E. coli was reported in 2015 by Budisa and Söll. Moreover, many biological phenomena, such as protein folding and stability, are based on synergistic effects at many positions in the protein sequence.
In this context, the SPI method generates recombinant protein variants or alloproteins directly by substitution of natural amino acids with unnatural counterparts. An amino acid auxotrophic expression host is supplemented with an amino acid analog during target protein expression. This approach avoids the pitfalls of suppression-based methods and it is superior to it in terms of efficiency, reproducibility and an extremely simple experimental setup. Numerous studies demonstrated how global substitution of canonical amino acids with various isosteric analogs caused minimal structural perturbations but dramatic changes in thermodynamic, folding, aggregation spectral properties and enzymatic activity.
in vitro synthesis
The genetic code expansion described above is in vivo. An alternative is the change of coding in vitro translation experiments. This requires the depletion of all tRNAs and the selective reintroduction of certain aminoacylated-tRNAs, some chemically aminoacylated.
Chemical synthesis
There are several techniques to produce peptides chemically, generally it is by solid-phase protection chemistry. This means that any (protected) amino acid can be added into the nascent sequence.
In November 2017, a team from the Scripps Research Institute reported having constructed a semi-synthetic E. coli bacteria genome using six different nucleotides (versus four found in nature). The two extra 'letters' form a third, unnatural base pair. The resulting organisms were able to thrive and synthesize proteins using "unnatural amino acids". The unnatural base pair used is dNaM–dTPT3. This unnatural base pair has been demonstrated previously, but this is the first report of transcription and translation of proteins using an unnatural base pair.
See also
Bioengineering
Directed evolution
Hachimoji DNA
List of genetic codes
Nucleic acid analogue
Non-proteinogenic amino acids
Protein labelling
Protein methods
Synthetic biology
Xenobiology
References
Molecular genetics
Nucleic acids
Synthetic biology | Expanded genetic code | [
"Chemistry",
"Engineering",
"Biology"
] | 6,813 | [
"Synthetic biology",
"Biomolecules by chemical classification",
"Biological engineering",
"Bioinformatics",
"Molecular genetics",
"Molecular biology",
"Nucleic acids"
] |
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