Statement.

Let be the prime-counting function that gives the number of primes less than or equal to, for any real number. For example, because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10. The prime number theorem then states that is a good approximation to (where log here means the natural logarithm), in the sense that the limit of the "quotient" of the two functions and as increases without bound is 1:  known as the asymptotic law of distribution of prime numbers. Using asymptotic notation this result can be restated as  This notation (and the theorem) does "not" say anything about the limit of the "difference" of the two functions as increases without bound. Instead, the theorem states that approximates in the sense that the relative error of this approximation approaches 0 as increases without bound.  The prime number theorem is equivalent to the statement that the th prime number satisfies  the asymptotic notation meaning, again, that the relative error of this approximation approaches 0 as increases without bound. For example, the th prime number is, and ()log() rounds to, a relative error of about 6.4%.  As outlined below, the prime number theorem is also equivalent to where and are the first and the second Chebyshev functions respectively.

History of the proof of the asymptotic law of prime numbers.

Based on the tables by Anton Felkel and Jurij Vega, Adrien-Marie Legendre conjectured in 1797 or 1798 that is approximated by the function, where and are unspecified constants. In the second edition of his book on number theory (1808) he then made a more precise conjecture, with and. Carl Friedrich Gauss considered the same question at age 15 or 16 "in the year 1792 or 1793", according to his own recollection in 1849. In 1838 Peter Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral (under the slightly different form of a series, which he communicated to Gauss). Both Legendre's and Dirichlet's formulas imply the same conjectured asymptotic equivalence of and stated above, although it turned out that Dirichlet's approximation is considerably better if one considers the differences instead of quotients.  In two papers from 1848 and 1850, the Russian mathematician Pafnuty Chebyshev attempted to prove the asymptotic law of distribution of prime numbers. His work is notable for the use of the zeta function, for real values of the argument "", as in works of Leonhard Euler, as early as 1737. Chebyshev's papers predated Riemann's celebrated memoir of 1859, and he succeeded in proving a slightly weaker form of the asymptotic law, namely, that if the limit as goes to infinity of exists at all, then it is necessarily equal to one. He was able to prove unconditionally that this ratio is bounded above and below by two explicitly given constants near 1, for all sufficiently large. Although Chebyshev's paper did not prove the Prime Number Theorem, his estimates for were strong enough for him to prove Bertrand's postulate that there exists a prime number between and for any integer.  An important paper concerning the distribution of prime numbers was Riemann's 1859 memoir "On the Number of Primes Less Than a Given Magnitude", the only paper he ever wrote on the subject. Riemann introduced new ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the analytically extended Riemann zeta function of a complex variable. In particular, it is in this paper of Riemann that the idea to apply methods of complex analysis to the study of the real function originates. Extending the ideas of Riemann, two proofs of the asymptotic law of the distribution of prime numbers were obtained independently by Jacques Hadamard and Charles Jean de la Vallée Poussin and appeared in the same year (1896). Both proofs used methods from complex analysis, establishing as a main step of the proof that the Riemann zeta function is non-zero for all complex values of the variable that have the form with.  During the 20th century, the theorem of Hadamard and de la Vallée Poussin also became known as the Prime Number Theorem. Several different proofs of it were found, including the "elementary" proofs of Atle Selberg and Paul Erdős (1949). While the original proofs of Hadamard and de la Vallée Poussin are long and elaborate, later proofs introduced various simplifications through the use of Tauberian theorems but remained difficult to digest. A short proof was discovered in 1980 by American mathematician Donald J. Newman. Newman's proof is arguably the simplest known proof of the theorem, although it is non-elementary in the sense that it uses Cauchy's integral theorem from complex analysis.

Proof sketch.

Here is a sketch of the proof referred to in one of Terence Tao's lectures. Like most proofs of the PNT, it starts out by reformulating the problem in terms of a less intuitive, but better-behaved, prime-counting function. The idea is to count the primes (or a related set such as the set of prime powers) with "weights" to arrive at a function with smoother asymptotic behavior. The most common such generalized counting function is the Chebyshev function, defined by  This is sometimes written as  where is the von Mangoldt function, namely  It is now relatively easy to check that the PNT is equivalent to the claim that Indeed, this follows from the easy estimates and (using big notation) for any,  The next step is to find a useful representation for. Let be the Riemann zeta function. It can be shown that is related to the von Mangoldt function, and hence to, via the relation  A delicate analysis of this equation and related properties of the zeta function, using the Mellin transform and Perron's formula, shows that for non-integer the equation  holds, where the sum is over all zeros (trivial and nontrivial) of the zeta function. This striking formula is one of the so-called explicit formulas of number theory, and is already suggestive of the result we wish to prove, since the term (claimed to be the correct asymptotic order of ) appears on the right-hand side, followed by (presumably) lower-order asymptotic terms.  The next step in the proof involves a study of the zeros of the zeta function. The trivial zeros −2, −4, −6, −8,... can be handled separately: which vanishes for a large. The nontrivial zeros, namely those on the critical strip, can potentially be of an asymptotic order comparable to the main term if, so we need to show that all zeros have real part strictly less than 1.  To do this, we take for granted that is meromorphic in the half-plane, and is analytic there except for a simple pole at, and that there is a product formula for. This product formula follows from the existence of unique prime factorization of integers, and shows that is never zero in this region, so that its logarithm is defined there and  Write ; then  Now observe the identity so that  for all. Suppose now that. Certainly is not zero, since has a simple pole at. Suppose that and let tend to 1 from above. Since formula_19 has a simple pole at and stays analytic, the left hand side in the previous inequality tends to 0, a contradiction.  Finally, we can conclude that the PNT is heuristically true. To rigorously complete the proof there are still serious technicalities to overcome, due to the fact that the summation over zeta zeros in the explicit formula for does not converge absolutely but only conditionally and in a "principal value" sense. There are several ways around this problem but many of them require rather delicate complex-analytic estimates. Edwards's book provides the details. Another method is to use Ikehara's Tauberian theorem, though this theorem is itself quite hard to prove. D. J. Newman observed that the full strength of Ikehara's theorem is not needed for the prime number theorem, and one can get away with a special case that is much easier to prove.

Prime-counting function in terms of the logarithmic integral.

In a handwritten note on a reprint of his 1838 paper "", which he mailed to Gauss, Dirichlet conjectured (under a slightly different form appealing to a series rather than an integral) that an even better approximation to is given by the offset logarithmic integral function, defined by  Indeed, this integral is strongly suggestive of the notion that the "density" of primes around should be. This function is related to the logarithm by the asymptotic expansion  So, the prime number theorem can also be written as. In fact, in another paper in 1899 de la Vallée Poussin proved that  for some positive constant, where is the big notation. This has been improved to  In 2016, Trudgian proved an explicit upper bound for the difference between formula_25 and formula_26: for formula_28.  Because of the connection between the Riemann zeta function and, the Riemann hypothesis has considerable importance in number theory: if established, it would yield a far better estimate of the error involved in the prime number theorem than is available today. More specifically, Helge von Koch showed in 1901 that if the Riemann hypothesis is true, the error term in the above relation can be improved to  (this last estimate is in fact equivalent to the Riemann hypothesis). The constant involved in the big notation was estimated in 1976 by Lowell Schoenfeld: assuming the Riemann hypothesis,  for all. He also derived a similar bound for the Chebyshev prime-counting function :  for all. This latter bound has been shown to express a variance to mean power law (when regarded as a random function over the integers), noise and to also correspond to the Tweedie compound Poisson distribution. Parenthetically, the Tweedie distributions represent a family of scale invariant distributions that serve as foci of convergence for a generalization of the central limit theorem.  The logarithmic integral is larger than for "small" values of. This is because it is (in some sense) counting not primes, but prime powers, where a power of a prime is counted as of a prime. This suggests that should usually be larger than by roughly, and in particular should always be larger than. However, in 1914, J. E. Littlewood proved that formula_32 changes sign infinitely often.

Elementary proofs.

In the first half of the twentieth century, some mathematicians (notably G. H. Hardy) believed that there exists a hierarchy of proof methods in mathematics depending on what sorts of numbers (integers, reals, complex) a proof requires, and that the prime number theorem (PNT) is a "deep" theorem by virtue of requiring complex analysis. This belief was somewhat shaken by a proof of the PNT based on Wiener's tauberian theorem, though this could be set aside if Wiener's theorem were deemed to have a "depth" equivalent to that of complex variable methods.  In March 1948, Atle Selberg established, by "elementary" means, the asymptotic formula  where  for primes. By July of that year, Selberg and Paul Erdős had each obtained elementary proofs of the PNT, both using Selberg's asymptotic formula as a starting point. These proofs effectively laid to rest the notion that the PNT was "deep", and showed that technically "elementary" methods were more powerful than had been believed to be the case. On the history of the elementary proofs of the PNT, including the Erdős–Selberg priority dispute, see an article by Dorian Goldfeld.  There is some debate about the significance of Erdős and Selberg's result. There is no rigorous and widely accepted definition of the notion of elementary proof in number theory, so it is not clear exactly in what sense their proof is "elementary". Although it does not use complex analysis, it is in fact much more technical than the standard proof of PNT. One possible definition of an "elementary" proof is "one that can be carried out in first order Peano arithmetic." There are number-theoretic statements (for example, the Paris–Harrington theorem) provable using second order but not first order methods, but such theorems are rare to date. Erdős and Selberg's proof can certainly be formalized in Peano arithmetic, and in 1994, Charalambos Cornaros and Costas Dimitracopoulos proved that their proof can be formalized in a very weak fragment of PA, namely, However, this does not address the question of whether or not the standard proof of PNT can be formalized in PA.

Computer verifications.

In 2005, Avigad "et al." employed the Isabelle theorem prover to devise a computer-verified variant of the Erdős–Selberg proof of the PNT. This was the first machine-verified proof of the PNT. Avigad chose to formalize the Erdős–Selberg proof rather than an analytic one because while Isabelle's library at the time could implement the notions of limit, derivative, and transcendental function, it had almost no theory of integration to speak of.  In 2009, John Harrison employed HOL Light to formalize a proof employing complex analysis. By developing the necessary analytic machinery, including the Cauchy integral formula, Harrison was able to formalize "a direct, modern and elegant proof instead of the more involved 'elementary' Erdős–Selberg argument".

Prime number theorem for arithmetic progressions.

Let denote the number of primes in the arithmetic progression less than. Dirichlet and Legendre conjectured, and de la Vallée Poussin proved, that, if and are coprime, then  where is Euler's totient function. In other words, the primes are distributed evenly among the residue classes modulo with 1. This is stronger than Dirichlet's theorem on arithmetic progressions (which only states that there is an infinity of primes in each class) and can be proved using similar methods used by Newman for his proof of the prime number theorem.  The Siegel–Walfisz theorem gives a good estimate for the distribution of primes in residue classes.

Prime number race.

Although we have in particular  empirically the primes congruent to 3 are more numerous and are nearly always ahead in this "prime number race"; the first reversal occurs at. However Littlewood showed in 1914 that there are infinitely many sign changes for the function  so the lead in the race switches back and forth infinitely many times. The phenomenon that is ahead most of the time is called Chebyshev's bias. The prime number race generalizes to other moduli and is the subject of much research; Pál Turán asked whether it is always the case that and change places when and are coprime to. Granville and Martin give a thorough exposition and survey.

Non-asymptotic bounds on the prime-counting function.

The prime number theorem is an "asymptotic" result. It gives an ineffective bound on as a direct consequence of the definition of the limit: for all, there is an such that for all,  However, better bounds on are known, for instance Pierre Dusart's The first inequality holds for all and the second one for.  A weaker but sometimes useful bound for is  In Pierre Dusart's thesis there are stronger versions of this type of inequality that are valid for larger. Later in 2010, Dusart proved:  The proof by de la Vallée Poussin implies the following. For every, there is an such that for all,

Approximations for the ""th prime number.

As a consequence of the prime number theorem, one gets an asymptotic expression for the th prime number, denoted by : A better approximation is Again considering the th prime number, this gives an estimate of ; the first 5 digits match and relative error is about 0.00005%.  Rosser's theorem states that This can be improved by the following pair of bounds:

Table of,, and.

The table compares exact values of to the two approximations and. The last column,, is the average prime gap below.  The value for was originally computed assuming the Riemann hypothesis; it has since been verified unconditionally.

Analogue for irreducible polynomials over a finite field.

There is an analogue of the prime number theorem that describes the "distribution" of irreducible polynomials over a finite field; the form it takes is strikingly similar to the case of the classical prime number theorem.  To state it precisely, let be the finite field with elements, for some fixed, and let be the number of monic "irreducible" polynomials over whose degree is equal to. That is, we are looking at polynomials with coefficients chosen from, which cannot be written as products of polynomials of smaller degree. In this setting, these polynomials play the role of the prime numbers, since all other monic polynomials are built up of products of them. One can then prove that If we make the substitution, then the right hand side is just which makes the analogy clearer. Since there are precisely monic polynomials of degree (including the reducible ones), this can be rephrased as follows: if a monic polynomial of degree is selected randomly, then the probability of it being irreducible is about.  One can even prove an analogue of the Riemann hypothesis, namely that  The proofs of these statements are far simpler than in the classical case. It involves a short, combinatorial argument, summarised as follows: every element of the degree extension of is a root of some irreducible polynomial whose degree divides ; by counting these roots in two different ways one establishes that where the sum is over all divisors of. Möbius inversion then yields where is the Möbius function. (This formula was known to Gauss.) The main term occurs for, and it is not difficult to bound the remaining terms. The "Riemann hypothesis" statement depends on the fact that the largest proper divisor of can be no larger than.

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function).

在数论中,素数定理描述素数在自然数中分布的渐进情况,给出随着数字的增大,质数的密度逐渐降低的直觉的形式化描述。1896年法国数学家雅克·阿达马和比利时数学家德拉瓦·莱普森(Charles Jean de la Vallée-Poussin)先后独立给出证明。证明用到了复分析,尤其是黎曼ζ函数。


Components and types.

The main part of such a system is made up of large pipes (i.e. the sewers, or "sanitary sewers") that convey the sewage from the point of production to the point of treatment or discharge.  Types of sanitary sewer systems that all usually are gravity sewers include:  Sanitary sewers not relying solely on gravity include:

Maintenance and rehabilitation.

Severe constraints are applied to sewerage, which may result in premature deterioration. These include root intrusion, joint displacement, cracks, and hole formations that lead to a significant volume of leakage with an overall risk for the environment and public health. For example, it is estimated that 500 million m of contaminated water per year can leak into soil and ground-water in Germany. The rehabilitation and replacement of damaged sewers is very costly. Annual rehabilitation costs for Los Angeles County are about €400 million, and in Germany, these costs are estimated to be €100 million. Hydrogen sulfide (HS) is indirectly responsible for biogenic sulfide corrosion and consequently, sewers need rehabilitation work. Various repair options are available to owners over a large range of costs and potential durability. One option is the application of a cementitious material based on calcium aluminate cement, after a cleaning of the corroded structure to remove loose material and contaminants in order to expose a sound, rough and clean substrate. Depending on the concrete condition and contamination, the cleaning can range from simple high pressure jet water cleaning (200 bar) up to real hydro-demolition (2000 bars).  One method to ensure sound concrete is exposed is to verify that the surface pH is superior to 10.  As for any concrete repair, the state-of-the-art rules must be followed. After this cleaning step, the cementitious material is applied to the saturated-surface-dry substrate using either:

Challenges.

Water table.

Sewer system infrastructure often reduces the water table in areas, especially in densely populated areas where rainwater (from house roofs) is directly piped into the system, as opposed to being allowed to be absorbed by the soil. In certain areas it has resulted in a significant lowering of the water table. In the example of Belgium, a lowering of the water table by 100 meters has been the result. The freshwater that is accumulated by the system is then piped to the sea.  In areas where this is a concern, vacuum sewers may be used instead, due to the shallow excavation that is possible for them.

Regulations.

In many European countries, citizens are obliged to connect their home sanitation to the national sewerage where possible. This has resulted in large percentages of the population being connected. For example, the Netherlands have 99% of the population connected to the system, and 1% has an individual sewage disposal system or treatment system, e.g., septic tank. Others have slightly lower (although still substantial) percentages; e.g., 96% for Germany.

Sewerage is the infrastructure that conveys sewage or surface runoff (stormwater, meltwater, rainwater) using sewers. It encompasses components such as receiving drains, manholes, pumping stations, storm overflows, and screening chambers of the combined sewer or sanitary sewer. Sewerage ends at the entry to a sewage treatment plant or at the point of discharge into the environment. It is the system of pipes, chambers, manholes, etc. that conveys the sewage or storm water.

下水道是都市公共设施之一,在古罗马时期就已经出现。以功能可分为污水下水道和雨水下水道。目前施工可以潜盾机方式施作,以减少施工期间对交通的影响。


Characteristics.

Living fossils have two main characteristics, although some have a third: The first two are required for recognition as a "living fossil" status; some authors also require the third, others merely note it as a frequent trait.  Such criteria are neither well-defined nor clearly quantifiable, but modern methods for analyzing evolutionary dynamics can document the distinctive tempo of stasis. Lineages that exhibit stasis over very short time scales are not considered living fossils; what is poorly-defined is the time scale over which the morphology must persist for that lineage to be recognized as a living fossil.  The term "living fossil" is much misunderstood in popular media in particular, in which it often is used meaninglessly. In professional literature the expression seldom appears and must be used with far more caution, although it has been used inconsistently.  One example of a concept that could be confused with "living fossil" is that of a "Lazarus taxon", but the two are not equivalent; a Lazarus taxon (whether a single species or a group of related species) is one that suddenly reappears, either in the fossil record or in nature, as if the fossil had "come to life again". In contrast to "Lazarus taxa", a living fossil in most senses is a species or lineage that has undergone exceptionally little change throughout a long fossil record, giving the impression that the extant taxon had remained identical through the entire fossil and modern period.  The average species turnover time, meaning the time between when a species first is established and when it finally disappears, varies widely among phyla, but averages about 2–3 million years. A living taxon that had long been thought to be extinct could be called a Lazarus taxon once it was discovered to be still extant. A dramatic example was the order Coelacanthiformes, of which the genus "Latimeria" was found to be extant in 1938. About that there is little debate — however, whether "Latimeria" resembles early members of its lineage sufficiently closely to be considered a living fossil as well as a Lazarus taxon has been denied by some authors in recent years.  Coelacanths disappeared from the fossil record some 80 million years ago (upper Cretaceous) and, to the extent that they exhibit low rates of morphological evolution, extant species qualify as living fossils. It must be emphasised that this criterion reflects fossil evidence, and is totally independent of whether the taxa had been subject to selection at all, which all living populations continuously are, whether they remain genetically unchanged or not. This in turn gives rise to a great deal of confusion; for one thing, the fossil record seldom preserves much more than the general morphology of a specimen — to determine much about its physiology is seldom possible. To determine much about its noncoding DNA is hardly ever possible, but even if a species were hypothetically unchanged in its physiology, it is to be expected from the very nature of the reproductive processes that its non-functional genomic changes would continue at more or less standard rates. It follows that a fossil lineage with apparently constant morphology need not imply equally constant physiology, for example, and certainly neither implies any cessation of the basic evolutionary processes such as natural selection, nor reduction in the usual rate of change of the noncoding DNA. In short, not even the most dramatic examples of living fossils can be expected to be without changes, no matter how persistently constant their fossils and their extant specimens might seem.  Some living fossils are taxa that were known from palaeontological fossils before living representatives were discovered. The most famous examples of this are: All the above include taxa that originally were described as fossils but now are known to include still-extant species.  Other examples of living fossils are single living species that have no close living relatives, but are survivors of large and widespread groups in the fossil record. For example: All of these were described from fossils before later found alive.  The fact that a living fossil is a surviving representative of an archaic lineage does not imply that it must retain all the "primitive" features (plesiomorphies) of its ancestral lineage. Although it is common to say that living fossils exhibit "morphological stasis", stasis, in the scientific literature, does not mean that any species is strictly identical to its ancestor, much less remote ancestors.  Some living fossils are relicts of formerly diverse and morphologically varied lineages, but not all survivors of ancient lineages necessarily are regarded as living fossils. See for example the uniquely and highly autapomorphic oxpeckers, which appear to be the only survivors of an ancient lineage related to starlings and mockingbirds.

Evolution and living fossils.

The term "living fossil" is usually reserved for species or larger clades that are exceptional for their lack of morphological diversity and their exceptional conservatism, and several hypotheses could explain morphological stasis on a geologically long time-scale. Early analyses of evolutionary rates emphasized the persistence of a taxon rather than rates of evolutionary change. Contemporary studies instead analyze rates and modes of phenotypic evolution, but most have focused on clades that are thought to be adaptive radiations rather than on those thought to be living fossils. Thus, very little is presently known about the evolutionary mechanisms that produce living fossils or how common they might be. Some recent studies have documented exceptionally low rates of ecological and phenotypic evolution despite rapid speciation. This has been termed a "non-adaptive radiation" referring to diversification not accompanied by adaptation into various significantly different niches. Such radiations are explanation for groups that are morphologically conservative. Persistent adaptation within an adaptive zone is a common explanation for morphological stasis. The subject of very low evolutionary rates, however, has received much less attention in the recent literature than that of high rates  Living fossils are not expected to exhibit exceptionally low rates of molecular evolution, and some studies have shown that they do not. For example, on tadpole shrimp ("Triops"), one article notes, "Our work shows that organisms with conservative body plans are constantly radiating, and presumably, adapting to novel conditions... I would favor retiring the term ‘living fossil’ altogether, as it is generally misleading."  The question posed by several recent studies pointed out that the morphological conservatism of coelacanths is not supported by paleontological data. In addition, it was shown recently that studies concluding that a slow rate of molecular evolution is linked to morphological conservatism in coelacanths are biased by the "a priori" hypothesis that these species are ‘living fossils’. Accordingly, the genome stasis hypothesis is challenged by the recent finding that the genome of the two extant coelacanth species "L. chalumnae" and "L. menadoensis" contain multiple species-specific insertions, indicating transposable element recent activity and contribution to post-speciation genome divergence. Such studies, however, challenge only a genome stasis hypothesis, not the hypothesis of exceptionally low rates of phenotypic evolution.

History.

The term was coined by Charles Darwin in his "On the Origin of Species" from 1859, when discussing "Ornithorhynchus" (the platypus) and "Lepidosiren" (the South American lungfish):

Other definitions.

Long-enduring.

A living taxon that lived through a large portion of geologic time.  Queensland lungfish ("Neoceratodus fosteri") is an example of an organism that meets this criterion. Fossils identical to modern Queensland lungfish have been dated at over 100 million years making this species one of the oldest if not actually the oldest extant vertebrate species.

Resembles ancient species.

A living taxon morphologically and/or physiologically resembling a fossil taxon through a large portion of geologic time (morphological stasis).

Retains many ancient traits.

A living taxon with many characteristics believed to be primitive.  This is a more neutral definition. However, it does not make it clear whether the taxon is truly old, or it simply has many plesiomorphies. Note that, as mentioned above, the converse may hold for true living fossil taxa; that is, they may possess a great many derived features (autapomorphies), and not be particularly "primitive" in appearance.

Relict population.

Any one of the above three definitions, but also with a relict distribution in refuges.  Some paleontologists believe that living fossils with large distributions (such as "Triops cancriformis") are not real living fossils. In the case of "Triops cancriformis" (living from the Triassic until now), the Triassic specimens lost most of their appendages (mostly only carapaces remain), and they have not been thoroughly examined since 1938.

Low diversity.

Any of the first three definitions, but the clade also has a low taxonomic diversity (low diversity lineages).  Oxpeckers are morphologically somewhat similar to starlings due to shared plesiomorphies, but are uniquely adapted to feed on parasites and blood of large land mammals, which has always obscured their relationships. This lineage forms part of a radiation that includes Sturnidae and Mimidae, but appears to be the most ancient of these groups. Biogeography strongly suggests that oxpeckers originated in eastern Asia and only later arrived in Africa, where they now have a relict distribution.  The two living species thus seem to represent an entirely extinct and (as Passerida go) rather ancient lineage, as certainly as this can be said in the absence of actual fossils. The latter is probably due to the fact that the oxpecker lineage never occurred in areas where conditions were good for fossilization of small bird bones, but of course, fossils of ancestral oxpeckers may one day turn up enabling this theory to be tested.

Operational definition.

An operational definition was proposed in 2017, where a 'living fossil' lineage has a slow rate of evolution and occurs close to the middle of morphological variation (the centroid of morphospace) among related taxa (i.e. a species is morphologically conservative among relatives). The scientific accuracy of the morphometric analyses used to classify tuatara as a living fossil under this definition have been criticised however, which prompted a rebuttal from the original authors.

Examples.

Some of these are informally known as "living fossils".

A living fossil is an extant taxon that closely resembles organisms otherwise known only from the fossil record. To be considered a living fossil, the fossil species must be old relative to the time of origin of the extant clade. Living fossils commonly are of species-poor lineages, but they need not be.

活化石,这个名词一开始是达尔文在1859年的"物种原始"一书中所提到的。 而对于活化石的定义各方的观点不一,例如:


Plot.

In a mansion called Xanadu, part of a vast palatial estate in Florida, the elderly Charles Foster Kane is on his deathbed. Holding a snow globe, he utters a word, "Rosebud", and dies; the globe slips from his hand and smashes on the floor. A newsreel obituary tells the life story of Kane, an enormously wealthy newspaper publisher. Kane's death becomes sensational news around the world, and the newsreel's producer tasks reporter Jerry Thompson with discovering the meaning of "Rosebud".  Thompson sets out to interview Kane's friends and associates. He tries to approach his wife, Susan Alexander Kane, now an alcoholic who runs her own nightclub, but she refuses to talk to him. Thompson goes to the private archive of the late banker Walter Parks Thatcher. Through Thatcher's written memoirs, Thompson learns that Kane's childhood began in poverty in Colorado.  In 1871, after a gold mine is discovered on her property, Kane's mother Mary Kane sends Charles away to live with Thatcher so that he would be properly educated. While Thatcher and Charles' parents discuss arrangements inside, the young Kane plays happily with a sled in the snow outside his parents' boarding-house and protests being sent to live with Thatcher. Furious at the prospect of exile from his own family to live with a man he does not know, the boy strikes Thatcher with his sled and attempts to run away.  Years later, after gaining full control over his trust fund at the age of 25, Kane enters the newspaper business and embarks

Cast.

The beginning of the film's ending credits state that "Most of the principal actors in "Citizen Kane" are new to motion pictures. The Mercury Theatre is proud to introduce them." The cast is listed in the following order:

Pre-production.

Development.

Hollywood had shown interest in Welles as early as 1936. He turned down three scripts sent to him by Warner Bros. In 1937, he declined offers from David O. Selznick, who asked him to head his film company's story department, and William Wyler, who wanted him for a supporting role in "Wuthering Heights". "Although the possibility of making huge amounts of money in Hollywood greatly attracted him," wrote biographer Frank Brady, "he was still totally, hopelessly, insanely in love with the theater, and it is there that he had every intention of remaining to make his mark."  Following "The War of the Worlds" broadcast of his CBS radio series "The Mercury Theatre on

Screenplay.

One of the long-standing controversies about "Citizen Kane" has been the authorship of the screenplay. Welles conceived the project with screenwriter Herman J. Mankiewicz, who was writing radio plays for Welles's CBS Radio series, "The Campbell Playhouse". Mankiewicz based the original outline on the life of William Randolph Hearst, whom he knew socially and came to hate after being exiled from Hearst's circle.  In February 1940 Welles supplied Mankiewicz with 300 pages of notes and put him under contract to write the first draft screenplay under the supervision of John Houseman,

Sources.

Welles never confirmed a principal source for the character of Charles Foster Kane. Houseman wrote that Kane is a synthesis of different personalities, with Hearst's life used as the main source. Some events and details were invented, and Houseman wrote that he and Mankiewicz also "grafted anecdotes from other giants of journalism, including Pulitzer, Northcliffe and Mank's first boss, Herbert Bayard Swope." Welles said, "Mr. Hearst was quite a bit like Kane, although Kane isn't really founded on Hearst in particular. Many people sat for it, so to speak". He specifically acknowledged that aspects of Kane were drawn from the lives of two business tycoons familiar from his youth in Chicago—Samuel Insull and Harold Fowler McCormick.  The character of Jedediah Leland was based on drama critic Ashton Stevens, George Stevens's uncle and Welles's close boyhood friend. Some detail came from Mankiewicz's own experience as a drama critic in New York.  The assumption that the character of Susan Alexander Kane was based on Marion Davies was a major reason Hearst tried to destroy "Citizen Kane". Welles denied that the character was based on Davies, whom he called "an extraordinary woman—nothing like the character Dorothy Comingore played in the movie." He cited Insull's building of the Chicago Opera House, and McCormick's lavish promotion of

Production.

Casting.

"Citizen Kane" was a rare film in that its principal roles were played by actors new to motion pictures. Ten were billed as Mercury Actors, members of the skilled repertory company assembled by Welles for the stage and radio performances of the Mercury Theatre, an independent theater company he founded with Houseman in 1937. "He loved to use the Mercury players," wrote biographer Charles Higham, "and consequently he launched several of them on movie careers."  The film represents the feature film debuts of William Alland, Ray Collins, Joseph Cotten, Agnes

Filming.

Production advisor Miriam Geiger quickly compiled a handmade film textbook for Welles, a practical reference book of film techniques that he studied carefully. He then taught himself filmmaking by matching its visual vocabulary to "The Cabinet of Dr. Caligari", which he ordered from the Museum of Modern Art, and films by Frank Capra, René Clair, Fritz Lang, King Vidor and Jean Renoir. The one film he genuinely studied was John Ford's "Stagecoach", which he watched 40 times. "As it turned out, the first day I ever walked onto a set was my first day as a director," Welles said. "I'd learned whatever I knew in the projection room—from Ford. After dinner every night for about a month, I'd run "Stagecoach", often with some different technician or department head from the studio, and ask questions. 'How was this done?' 'Why was this done?' It was like going to school."  Welles's cinematographer for the film was Gregg Toland, described by Welles as "just then, the number-one cameraman in the world." To Welles's astonishment, Toland visited him at his office and said, "I want you to use me on your picture." He had seen some of the Mercury stage productions (including "Caesar") and said he wanted to work with someone who had never made a movie. RKO hired Toland on loan from Samuel Goldwyn Productions in the first week of June

Post-production.

"Citizen Kane" was edited by Robert Wise and assistant editor Mark Robson. Both would become successful film directors. Wise was hired after Welles finished shooting the "camera tests" and began officially making the film. Wise said that Welles "had an older editor assigned to him for those tests and evidently he was not too happy and asked to have somebody else. I was roughly Orson's age and had several good credits." Wise and Robson began editing the film while it was still shooting and said that they "could tell certainly that we were getting something very special. It was outstanding film day in and day out."  Welles gave Wise detailed instructions and was usually not present during the film's editing. The film was very well planned out and intentionally shot for such post-production techniques as slow dissolves. The lack of coverage made editing

Trailer.

Written and directed by Welles at Toland's suggestion, the theatrical trailer for "Citizen Kane" differs from other trailers in that it did not feature a single second of footage of the actual film itself, but acts as a wholly original, tongue-in-cheek, pseudo-documentary piece on the film's production. Filmed at the same time as "Citizen Kane" itself, it offers the only existing behind-the-scenes footage of the film. The trailer, shot by Wild instead of Toland, follows an unseen Welles as he provides narration for a tour around the film set, introductions to the film's

Style.

Film scholars and historians view "Citizen Kane" as Welles's attempt to create a new style of filmmaking by studying various forms of it and combining them into one. However, Welles stated that his love for cinema began only when he started working on the film. When asked where he got the confidence as a first-time director to direct a film so radically different from contemporary cinema, he responded, "Ignorance, ignorance, sheer ignorance—you know there's no confidence to equal it. It's only when you know something about a profession, I think, that you're timid or careful."  David Bordwell wrote that "The best way to understand "Citizen Kane" is to stop worshiping it as a triumph of technique." Bordwell argues that the film did not invent any of its famous techniques such as deep focus cinematography, shots of the ceilings, chiaroscuro lighting and temporal jump-cuts, and that many of these stylistics had been used in German Expressionist films of the 1920s, such as "The Cabinet of Dr. Caligari". But Bordwell asserts that the film did put them all together for the first time and perfected the medium in one single film. In a 1948 interview, D. W. Griffith said, "I loved "Citizen Kane" and particularly loved the ideas he took from me."  Arguments against the film's cinematic innovations were made as early as 1946 when French historian Georges Sadoul wrote, "The film is an encyclopedia of old techniques." He pointed out such examples as compositions that used both the foreground and the background in the films of Auguste and Louis Lumière, special effects used in the films of Georges Méliès, shots of the ceiling in Erich von Stroheim's "Greed" and newsreel montages in the films of Dziga Vertov.  French film critic André Bazin defended the film, writing: "In this respect, the accusation of plagiarism could very well be extended to the film's use of panchromatic film or its exploitation of the properties of gelatinous silver halide." Bazin disagreed with Sadoul's comparison to Lumière's cinematography since "Citizen Kane" used more sophisticated lenses, but acknowledged that it had similarities to such previous works as "The 49th Parallel" and "The Power and the Glory". Bazin stated that "even if Welles did not invent the cinematic devices employed in "Citizen Kane", one should nevertheless credit him with the invention of their "meaning"." Bazin championed the techniques in the film for its depiction of heightened reality, but Bordwell believed that the film's use of special effects contradicted some of Bazin's theories.

Political themes.

Laura Mulvey explored the anti-fascist themes of "Citizen Kane" in her 1992 monograph for the British Film Institute. The "News on the March" newsreel presents Kane keeping company with Hitler and other dictators while he smugly assures the public that there will be no war. She wrote that the film reflects "the battle between intervention and isolationism" then being waged in the United States; the film was released six months before the attack on Pearl Harbor, while President Franklin

Reception.

Pre-release controversy.

To ensure that Hearst's life's influence on "Citizen Kane" was a secret, Welles limited access to dailies and managed the film's publicity. A December 1940 feature story in "Stage" magazine compared the film's narrative to "Faust" and made no mention of Hearst.  The film was scheduled to premiere at RKO's flagship theater Radio City Music Hall on February 14, but in early January 1941 Welles was not finished with post-production work and told RKO that it still needed its musical score. Writers for national magazines had early deadlines and so a rough cut was previewed for a select few on January 3, 1941 for such magazines as "Life", "Look" and "Redbook". Gossip columnist Hedda Hopper (an arch-rival of Louella Parsons, the Hollywood correspondent for

Hearst's response.

Hearing about "Citizen Kane" enraged Hearst so much that he banned any advertising, reviewing, or mentioning of it in his papers, and had his journalists libel Welles. Welles used Hearst's opposition as a pretext for previewing the film in several opinion-making screenings in Los Angeles, lobbying for its artistic worth against the hostile campaign that Hearst was waging. A special press screening took place in early March. Henry Luce was in attendance and reportedly wanted to buy the film from RKO for $1 million to distribute it himself. The reviews for this screening were positive. A "Hollywood Review" headline read, "Mr. Genius Comes Through; 'Kane' Astonishing Picture". The "Motion Picture Herald" reported about the screening and Hearst's intention to

Release.

Radio City Music Hall's management refused to screen "Citizen Kane" for its premiere. A possible factor was Parsons's threat that "The American Weekly" would run a defamatory story on the grandfather of major RKO stockholder Nelson Rockefeller. Other exhibitors feared being sued for libel by Hearst and refused to show the film. In March Welles threatened the RKO board of governors with a lawsuit if they did not release the film. Schaefer stood by Welles and opposed the board of governors. When RKO still delayed the film's release Welles offered to buy the film for $1 million and the studio finally agreed to release the film on May 1.  Schaefer managed to book a few theaters willing to show

Contemporary responses.

"Citizen Kane" received good reviews from several critics. "New York Daily News" critic Kate Cameron called it "one of the most interesting and technically superior films that has ever come out of a Hollywood studio". "New York World-Telegram" critic William Boehnel said that the film was "staggering and belongs at once among the greatest screen achievements". "Time" magazine wrote that "it has found important new techniques in picture-making and story-telling." "Life" magazine's review said that "few movies have ever come from Hollywood with such powerful narrative, such original technique, such exciting photography." John C. Mosher of "The New Yorker" called the film's style "like fresh air" and raved "Something new has come to the

Accolades.

It was widely believed the film would win most of its Academy Award nominations, but it received only the award for Best Original

Legacy.

"Citizen Kane" was the only film made under Welles's original contract with RKO Pictures, which gave him complete creative control. Welles's new business manager and attorney permitted the contract to lapse. In July 1941, Welles reluctantly signed a new and less favorable deal with RKO under which he produced and directed "The Magnificent Ambersons" (1942), produced "Journey into Fear" (1943), and began "It's All True", a film he agreed to do without payment. In the new contract Welles was an employee of the studio and lost the right to final cut, which later allowed RKO to modify and re-cut "The Magnificent Ambersons" over his objections. In June 1942 Schaefer resigned the presidency of RKO Pictures and Welles's contract was terminated by his successor.

Release in Europe.

During World War II, "Citizen Kane" was not seen in most European countries. It was shown in France for the first time on July 10, 1946 at the Marbeuf theater in Paris. Initially most French film critics were influenced by the negative reviews of Jean-Paul Sartre in 1945 and Georges Sadoul in 1946. At that time many French intellectuals and filmmakers shared Sartre's negative opinion that Hollywood filmmakers were uncultured. Sartre criticized the film's flashbacks for its nostalgic and romantic preoccupation with the past instead of the realities of the present and said that "the whole film is based on a misconception of what cinema is all about. The film is in

Re-evaluation.

By 1942 "Citizen Kane" had run its course theatrically and, apart from a few showings at big city arthouse cinemas, it largely vanished and both the film's and Welles's reputation fell among American critics. In 1949 critic Richard Griffith in his overview of cinema, "The Film Till Now", dismissed "Citizen Kane" as "... tinpot if not crackpot Freud."  In the United States, it was neglected and forgotten until its revival on television in the mid-1950s. Three key events in 1956 led to its re-evaluation in the United States: first, RKO was one of the first studios to sell its library to television, and early that year "Citizen Kane" started to appear on television; second, the film was re-released theatrically to coincide with Welles's return to the New

Influence.

"Citizen Kane" has been called the most influential film of all time. Richard Corliss has asserted that Jules Dassin's 1941 film "The Tell-Tale Heart" was the first example of its influence and the first pop culture reference to the film occurred later in 1941 when the spoof comedy "Hellzapoppin'" featured a "Rosebud" sled. The film's cinematography was almost immediately influential and in 1942 "American Cinematographer" wrote "without a doubt the most immediately noticeable trend in cinematography methods during the year was the trend toward crisper definition and increased depth of field."  The cinematography influenced John Huston's "The Maltese Falcon". Cinematographer Arthur Edeson used a wider-angle lens than Toland and the film includes many long takes, low angles and shots of the ceiling, but it did not use deep focus shots on large sets to the extent that "Citizen Kane" did. Edeson and Toland are often credited together for revolutionizing cinematography in 1941. Toland's cinematography influenced his own work on "The Best Years of Our Lives". Other films influenced include "Gaslight", "Mildred

Film memorabilia.

In 1982, film director Steven Spielberg bought a "Rosebud" sled for $60,500; it was one of three balsa sleds used in the closing scenes and the only one that was not burned. After the Spielberg purchase, it was reported that retiree Arthur Bauer claimed to own another "Rosebud" sled. In early 1942, when Bauer was 12, he had won an RKO publicity contest and selected the hardwood sled as his prize. In 1996, Bauer's estate offered the painted pine sled at auction through Christie's. Bauer's son told CBS News that his mother had once wanted to paint the sled and use it as a plant stand, but Bauer told her to "just save it and put it in the closet." The sled was sold to an anonymous bidder for $233,500.  Welles's Oscar for Best Original Screenplay was believed to be lost until it was rediscovered

Rights and home media.

The composited camera negative of "Citizen Kane" was destroyed in a New Jersey film laboratory fire in the 1970s. Subsequent prints were derived from a master positive (a fine-grain preservation element) made in the 1940s and originally intended for use in overseas distribution. Modern techniques were used to produce a pristine print for a 50th Anniversary theatrical reissue in 1991 which Paramount Pictures released for then-owner Turner Broadcasting System, which earned $1.6 million in North America.  In 1955, RKO sold the American television rights to its film library, including "Citizen Kane", to C&C Television Corp. In 1960, television rights to the pre-1959 RKO's live-action library were acquired by United Artists. RKO kept the non-broadcast television rights to its library.  In 1976, when home video was in its infancy, entrepreneur Snuff Garrett bought cassette rights to the RKO library for what United Press International termed "a pittance." In 1978 The Nostalgia Merchant released the film through Media Home Entertainment. By 1980 the 800-title library of The Nostalgia Merchant was earning $2.3 million a year. "Nobody wanted cassettes four years ago," Garrett told UPI. "It wasn't the first time people called me crazy. It was a hobby with me which became big business." RKO Home Video released the film on VHS and Betamax in 1985.  In 1984, The Criterion Collection released the film as its first LaserDisc. It was made from a fine grain master positive provided by the UCLA Film and Television Archive. When told about the then-new concept of having an audio commentary on the disc, Welles was skeptical but said "theoretically, that's good for teaching movies, so long as they don't talk nonsense." In 1992 Criterion released a new 50th Anniversary Edition LaserDisc. This version had an improved transfer and additional special features, including the documentary "The Legacy of Citizen Kane" and Welles's early short "The Hearts of Age".  Turner Broadcasting System acquired broadcast television rights to the RKO library in 1986 and the full worldwide rights to the library in 1987. The RKO Home Video unit was reorganized into Turner Home Entertainment that year. In 1991 Turner released a 50th Anniversary Edition on VHS and as a collector's edition that includes the film, the documentary "Reflections On Citizen Kane", Harlan Lebo's 50th anniversary album, a poster and a copy of the original script. In 1996, Time Warner acquired Turner and Warner Home Video absorbed Turner Home Entertainment. In 2011 WarnerMedia's Warner Bros. unit had distribution rights for the film.  In 2001, Warner Home Video released a 60th Anniversary Collectors Edition DVD. The two-disc DVD included feature-length commentaries by Roger Ebert and Peter Bogdanovich, as well as a second DVD with the feature length documentary "The Battle Over Citizen Kane" (1999). It was simultaneously released on VHS. The DVD was criticized for being ""too" bright, "too clean"; the dirt and grime had been cleared away, but so had a good deal of the texture, the depth, and the sense of film grain."  In 2003, Welles's daughter Beatrice Welles sued Turner Entertainment, claiming the Welles estate is the legal copyright holder of the film. She claimed that Welles's deal to terminate his contracts with RKO meant that Turner's copyright of the film was null and void. She also claimed that the estate of Orson Welles was owed 20% of the film's profits if her copyright claim was not upheld. In 2007 she was allowed to proceed with the lawsuit, overturning the 2004 decision in favor of Turner Entertainment on the issue of video rights.  In 2011, it was released on Blu-ray and DVD in a 70th Anniversary Edition. The "San Francisco Chronicle" called it "the Blu-ray release of the year." Supplements included everything available on the 2001 Warner Home Video release, including "The Battle Over Citizen Kane" DVD. A 70th Anniversary Ultimate Collector's Edition added a third DVD with "RKO 281" (1999), an award winning TV movie about the making of the film. Its packaging extras included a hardcover book and a folio containing mini reproductions of the original souvenir program, lobby cards, and production memos and correspondence. The transfer for the US releases were scanned as 4K resolution from three different 35mm prints and rectified the quality issues of the 2001 DVD. The rest of the world continued to receive home video releases based on the older transfer. This was partially rectified in 2016 with the release of the 75th Anniversary Edition in both the UK and US, which was a straight repackaging of the main disc from the 70th Anniversary Edition.

External links.

Database  Other

Citizen Kane is a 1941 American drama film by Orson Welles, its producer, co-screenwriter, director and star. The picture was Welles's first feature film. Nominated for Academy Awards in nine categories, it won an Academy Award for Best Writing (Original Screenplay) by Herman J. Mankiewicz and Welles. Considered by many critics, filmmakers, and fans to be the greatest film ever made, "Citizen Kane" was voted as such in five consecutive British Film Institute "Sight & Sound" polls of critics, and it topped the American Film Institute's 100 Years... 100 Movies list in 1998, as well as its 2007 update. "Citizen Kane" is particularly praised for Gregg Toland's cinematography, Robert Wise's editing, Bernard Herrmann's music, and its narrative structure, all of which have been considered innovative and precedent-setting.

《公民凯恩》(英语:"Citizen Kane",又译-{zh-hant:公民凯恩;zh-hans:大国民}-)是奥森·威尔士于1940年拍摄,1941年由美国RKO(雷电华)电影公司出品的剧情片。影片讲述报业大王查尔斯·大众特·凯恩的一生。由奥森·威尔士担任导演、制片、编剧(之一)以及主演。曾获得1941年美国电影科学与艺术学院奖(即奥斯卡奖)九项提名,并最终获得最佳原著剧本奖。


Etymology.

The name "Shoshone" comes from "Sosoni", a Shoshone word for high-growing grasses. Some neighboring tribes call the Shoshone "Grass House People," based on their traditional homes made from "sosoni". Shoshones call themselves "Newe", meaning "People."  Meriwether Lewis recorded the tribe as the "Sosonees or snake Indians" in 1805.

Language.

The Shoshoni language is spoken by approximately 1,000 people today. It belongs to the Central Numic branch of the Uto-Aztecan language family. Speakers are scattered from central Nevada to central Wyoming.  The largest numbers of Shoshoni speakers live on the federally recognized Duck Valley Indian Reservation, located on the border of Nevada and Idaho; and Goshute Reservation in Utah. Idaho State University also offers Shoshoni-language classes.

History.

The Shoshone are a Native American tribe, who originated in the western Great Basin and spread north and east into present-day Idaho and Wyoming. By 1500, some Eastern Shoshone had crossed the Rocky Mountains into the Great Plains. After 1750, warfare and pressure from the Blackfoot, Crow, Lakota, Cheyenne, and Arapaho pushed Eastern Shoshone south and westward. Some of them moved as far south as Texas, emerging as the Comanche by 1700.  As more European-American settlers migrated west, tensions rose with the indigenous people over competition for territory and resources. Wars occurred throughout the second half of the 19th century. The Northern Shoshone, led by Chief Pocatello, fought during the 1860s with settlers in Idaho (where the city Pocatello was named for him). As more settlers encroached on Shoshone hunting territory, the natives raided farms and ranches for food and attacked immigrants.  The warfare resulted in the Bear River Massacre (1863) when US forces attacked and killed an estimated 410 Northwestern Shoshone, who were at their winter encampment. A large number of the dead were civilians, including women and children, deliberately killed by the soldiers. This was the highest number of deaths which the Shoshone suffered at the hands of United States forces.  During the American Civil War travelers continued to migrate westward along the Westward Expansion Trails. When the Shoshone, along with the Utes participated in attacks on the mail route that ran west out of Fort Laramie, the mail route had to be relocated south of the trail through Wyoming.  Allied with the Bannock, to whom they were related, the Shoshone fought against the United States in the Snake War from 1864 to 1868. They fought US forces together in 1878 in the Bannock War. In 1876, by contrast, the Shoshone fought alongside the U.S. Army in the Battle of the Rosebud against their traditional enemies, the Lakota and Cheyenne.  In 1879 a band of approximately 300 Eastern Shoshone (known as "Sheepeaters") became involved in the Sheepeater Indian War. It was the last Indian war fought in the Pacific Northwest region of the present-day United States.  In 1911 a small group of Bannock under a leader named Mike Daggett, also known as "Shoshone Mike," killed four ranchers in Washoe County, Nevada. The settlers formed a posse and went out after the Native Americans. They caught up with the Bannock band on February 26, 1911 and killed eight. They lost one man of the posse, Ed Hogle. The posse captured three children and a woman.  A rancher donated the partial remains of three adult males, two adult females, two adolescent males, and three children (believed to be Shoshone Mike and his family, according to contemporary accounts) to the Smithsonian Institution in Washington, DC for study. In 1994, the institution repatriated the remains to the Fort Hall Idaho Shoshone-Bannock Tribe.  In 2008 the Northwestern Band of the Shoshone Nation acquired the site of the Bear River Massacre and some surrounding land. They wanted to protect the holy land and to build a memorial to the massacre, the largest their nation had suffered. "In partnership with the American West Heritage Center and state leaders in Idaho and Utah, the tribe has developed public/private partnerships to advance tribal cultural preservation and economic development goals." They have become a leader in developing tribal renewable energy.

Historical population.

In 1845 the estimated population of Northern and Western Shoshone was 4,500, much reduced after they had suffered infectious disease epidemics and warfare. The completion of the First Transcontinental Railroad in 1869 was followed by European-American immigrants arriving in unprecedented numbers in the territory.  In 1937 the Bureau of Indian Affairs counted 3,650 Northern Shoshone and 1,201 Western Shoshone. As of the 2000 census, some 12,000 persons identified as Shoshone.

Bands.

Shoshone people are divided into traditional bands based both on their homelands and primary food sources. These include:

The Shoshone or Shoshoni ( or ) are a Native American tribe with four large cultural/linguistic divisions:

休休尼(Shoshone)( or ) 是个曾经活跃于北美洲美国西部与墨西哥北部的大部族,分为三大部落;本族语言是休休尼语。此语属犹他-阿兹提克语系中的Numic语。


Biological membranes.

An example of a biological semi-permeable membrane is the lipid bilayer, on which is based on the plasma membrane that surrounds all biological cells. A group of phospholipids (consisting of a phosphate head and two fatty acid tails) arranged into a double layer, the phospholipid bilayer is a semipermeable membrane that is very specific in its permeability. The hydrophilic phosphate heads are in the outside layer and exposed to the water content outside and within the cell. The hydrophobic tails are the layer hidden in the inside of the membrane. The phospholipid bilayer is most permeable to small, uncharged solutes. Protein channels float through the phospholipids, and, collectively, this model is known as the fluid mosaic model. Aquaporins are protein channel pores permeable to HO water.

Reverse osmosis.

The diffusion of water through a selectively permeable membrane is called osmosis. This allows only certain particles to go through including water and leaving behind the solutes including salt and other contaminants. In the process of reverse osmosis, thin film composite membranes (TFC or TFM) are used. These are semipermeable membranes manufactured principally for use in water purification or desalination systems. They also have use in chemical applications such as batteries and fuel cells. In essence, a TFC material is a molecular sieve constructed in the form of a film from two or more layered materials. Prof. Sidney Loeb and Srinivasa Sourirajan invented the first practical synthetic semi-permeable membrane. Membranes used in reverse osmosis are, in general, made out of polyamide, chosen primarily for its permeability to water and relative impermeability to various dissolved impurities including salt ions and other small molecules that cannot be filtered. Another example of a semipermeable membrane is dialysis tubing.

Role in cellular communication.

The semipermeable membrane is pertinent to cellular communication. A cell membrane consists of proteins and phospholipids. Signaling molecules send chemical messages to the proteins in the cell membrane. The signaling molecules bind to proteins, which alters the protein structure. A change in the protein structure initiates a signalling cascade. An example of a technique that leverages membrane-based are tissue & cellular preservation technologies which show that adherent cells such as stem cells and myoblasts have better outcomes than non-adherent cells due to persistent signalling before and after preservation.

Other types.

Other types of semipermeable membranes are cation exchange membrane (CEM), charge mosaic membrane (CMM), bipolar membrane (BPM), anion exchange membrane (AEM) alkali anion exchange membrane (AAEM) and proton exchange membrane (PEM).

Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by diffusion—or occasionally by more specialized processes of facilitated diffusion, passive transport or active transport. The rate of passage depends on the pressure, concentration, and temperature of the molecules or solutes on either side, as well as the permeability of the membrane to each solute. Depending on the membrane and the solute, permeability may depend on solute size, solubility, properties, or chemistry. How the membrane is constructed to be selective in its permeability will determine the rate and the permeability. Many natural and synthetic materials thicker than a membrane are also semipermeable. One example of this is the thin film on the inside of the egg. Note that a semipermeable membrane is not the same as a selectively permeable membrane. Semipermeable membrane describes a membrane that allows some particles to pass through (by size), whereas the selectively permeable membrane "chooses" what passes through (size is not a factor).

半透膜semi-permeable membrane,并不是选透膜selectively permeable membrane,半透膜根据分子/离子的物理特性,例如大小size,电荷charge决定是否可以通过。而物质通过渗透,被动转运,主动转运通过膜。通过率取决于两侧分子/离子的压力,浓度和温度。


History.

18th and 19th century.

In 1802, John Feltham wrote a version of the history of porter that has been used as the basis for most writings on the topic. Very little of Feltham's story is backed up by contemporary evidence; his account is based on a letter written by Obadiah Poundage (who had worked for decades in the London brewing trade) in the 1760s. Feltham badly misinterpreted parts of the text, mainly due to his unfamiliarity with 18th-century brewing terminology. Feltham claimed that in 18th-century London a popular beverage called three threads was made consisting of a third of a pint each of ale, beer and twopenny (the strongest beer, costing two pence a quart). About 1730, Feltham said, a brewer called Harwood made a single beer called Entire or Entire butt, which recreated the flavour of "three threads" and became known as "porter".  Porter is mentioned as early as 1721, but no writer before Feltham says it was made to replicate "three threads". Instead, it seems to be a more-aged development of the brown beers already being made in London. Before 1700, London brewers sent out their beer very young and any ageing was either performed by the publican or a dealer. Porter was the first beer to be aged at the brewery and dispatched in a condition fit to be drunk immediately. It was the first beer that could be made on any large scale, and the London porter brewers, such as Whitbread, Truman, Parsons and Thrale, achieved great success financially.  Early London porters were strong beers by modern standards. Early trials with the hydrometer in the 1770s recorded porter as having an OG (original gravity) of 1.071 and 6.6% ABV. Increased taxation during the Napoleonic Wars pushed its gravity down to around 1.055, where it remained for the rest of the 19th century. The popularity of the style prompted brewers to produce porters in a wide variety of strengths. These started with Single Stout Porter at around 1.066, Double Stout Porter (such as Guinness) at 1.072, Triple Stout Porter at 1.078 and Imperial Stout Porter at 1.095 and more. As the 19th century progressed the porter suffix was gradually dropped.  The large London porter breweries pioneered many technological advances, such as the use of the thermometer (about 1760) and the hydrometer (1770). The use of the latter transformed the nature of porter. The first porters were brewed from 100% brown malt. Now brewers were able to accurately measure the yield of the malt they used, and noticed that brown malt, though cheaper than pale malt, only produced about two-thirds as much fermentable material. When the malt tax was increased to help pay for the Napoleonic War, brewers had an incentive to use less malt. Their solution was to use a proportion of pale malt and add colouring to obtain the expected hue. When a law was passed in 1816 allowing only malt and hops to be used in the production of beer (a sort of British Reinheitsgebot), they were left in a quandary. Their problem was solved by Wheeler's invention of the almost black (kilned) patent malt in 1817. It was now possible to brew porter from 95% pale malt and 5% patent malt, though most London brewers continued to use some brown malt for flavour.  Until about 1800, all London porter was matured in large vats, often holding several hundred barrels, for between six and eighteen months before being racked into smaller casks to be delivered to pubs. It was discovered that it was unnecessary to age all porter. A small quantity of highly aged beer (18 months or more) mixed with fresh or "mild" porter produced a flavour similar to that of aged beer. It was a cheaper method of producing porter, as it required less beer to be stored for long periods. The normal blend was around two parts young beer to one part old.  After 1860, as the popularity of porter and the aged taste began to wane, porter was increasingly sold "mild". In the final decades of the century, many breweries discontinued their porter, but continued to brew one or two stouts. Those that persisted with porter, brewed it weaker and with fewer hops. Between 1860 and 1914, the gravity dropped from 1.058 to 1.050 and the hopping rate from two pounds to one pound per 36 gallon barrel.

20th and 21st century.

During the First World War in Britain, shortages of grain led to restrictions on the strength of beer. Less strict rules were applied in Ireland, allowing Irish brewers such as Guinness to continue to brew beers closer to pre-war strengths. English breweries continued to brew a range of bottled, and sometimes draught, stouts until the Second World War and beyond. During the Second World War, because of the Irish Free State's official policy of neutrality, this period was not technically considered wartime, however the country suffered similar resource scarcities and consequent rationing to the United Kingdom, thus this period was officially named The Emergency there. They were considerably weaker than the pre-war versions (down from 1.055–1.060 to 1.040–1.042) and around the strength that porter had been in 1914. The drinking of porter, with its strength slot now occupied by single stout, steadily declined, and the last porter was produced in 1941.  The Anchor Brewing Company started brewing a Porter in 1972 and was bottled in 1974 that kickstarted the revival of the style which began in 1978, when the Penrhos microbrewery introduced a porter. A little later, Timothy Taylor began to brew a porter as well. There are now dozens of breweries in Britain making porter, with Fuller's London Porter winning gold and silver medals at the 1999, 2000 and 2002 International Beer & Cider Competitions, and CAMRA's Supreme Champion Winter Beer of Britain silver medal in 2007, with Wickwar Brewery's Station Porter winning gold in 2008.  Many breweries brew porters in wide varieties, including, but not limited to, pumpkin, honey, vanilla, plum, and chocolate. Specialized porter brews continue the tradition of ageing in barrels, and the use of bourbon barrels is not uncommon.

Ireland.

Porter was first brewed in Ireland in 1776 and, although Arthur Guinness did not start brewing until 1787, he had phased out all other types of beer from his Guinness Brewery by 1799. Beamish and Crawford in Cork and Murphy's Brewery followed suit and abandoned ales in favour of porter. The move from porter to stout was made when Arthur Guinness realised that he would pay less tax if he used unmalted and roasted barley in his beer.  In Ireland, especially Dublin, the porter was known as "plain porter" or just "plain". This is the drink referred to in Flann O'Brien's poem "The Workman's Friend": "A pint of plain is your only man." By contrast, extra-strong porter was called "Stout Porter". The last Guinness Irish porter was produced in 1974, though the company launched a "revival" based upon a 1796 recipe in 2014.  After the invention of malted barley roasted until black to impart a darker colour and distinct burnt taste to the beer in 1817, Irish brewers dropped the use of brown malt, using patent malt and pale malt only, while English brewers continued using some brown malt, giving a difference in style between English and Irish porters.

United States.

Porter was being commercially brewed in the United States in the 18th century, especially in New England and Pennsylvania. After the introduction of lagers in the United States in the 1850s, breweries began brewing their porters with lager yeast rather than a top-fermenting one. In addition, these American porters often included adjuncts such as maize, molasses, and Porterine. Porterine was developed in America as a brewer's tool, added in the wort of lighter beers, to add colour and flavour which emulate that of a porter. Porterine is made from the slow cooking of corn syrup, which concentrates the sugars in the substance. With this concentration comes the caramel-like colour and consistency of Porterine. With the advent of the craft brewing movement, many microbreweries produce porters and stouts with traditional methods as well as the American techniques.

Baltic porter.

Baltic porter is a version of imperial stout which originated in the Baltic region in the 19th century. Imperial stouts exported from Britain in the 18th century were popular in the countries around the Baltic Sea, and were recreated locally using local ingredients and brewing traditions. Early versions were warm fermented until the late 19th century when many breweries began to brew their porter with cool fermentation. Baltic porters typically have a minimum gravity of 18 degrees plato and a high alcohol content, even over 10% abv. They are produced in Finland, Estonia, Latvia, Lithuania, the Czech Republic, Germany, Poland, Russia, Ukraine, Denmark, Sweden and the United States.  Baltic porter is a specialty of many Polish breweries, with the country's oldest being produced by Żywiec in 1881. Finland's Sinebrychoff has been brewing Baltic porters in Helsinki since the 1860s, while Estonia's Põhjala is a newcomer specialising in barrel-aged porters. In Denmark the word "porter" is synonymous with "imperial stout" and Wiibroe's Baltic porter (now brewed by Carlsberg) is known by both names. Porter was brewed in Germany from 1853 until 1990, when production ceased in East Germany after reunification. In 1998, the Hoepfner brewery of Karlsruhe resumed production of an old recipe. It was followed by other brewers such as Neuzeller Kloster Brewery and Bergquell Brewery who brew an 8% abv Baltic porter.  Baltic Porter Day, started in Poland in 2016 by Marcin Chmielarz, is celebrated annually on the third Saturday of January.

Porter is a style of beer that was developed in London, England in the early eighteenth century. It was well-hopped and dark in appearance due to the use of brown malt. The name originated due to its popularity with street and river porters.

波特(英语:Porter),又译为波打,一种深色的啤酒,源自于18世纪英国伦敦地区。它是由棕色爱尔啤酒(Brown ale)改良而来,以烤过的麦芽发酵而成。它广受河上及街道搬运工(porter)的欢迎,因此得名。


Formal definition.

Probability mass function is the probability distribution of a discrete random variable, and provides the possible values and their associated probabilities. It is the function formula_1 formula_2 defined by for formula_3, where formula_4 is a probability measure. formula_5 can also be simplified as formula_6.  The probabilities associated with each possible values must be positive and sum up to 1. For all other values, the probabilities need to be 0.  Thinking of probability as mass helps to avoid mistakes since the physical mass is conserved as is the total probability for all hypothetical outcomes formula_10.

Measure theoretic formulation.

A probability mass function of a discrete random variable formula_11 can be seen as a special case of two more general measure theoretic constructions: the distribution of formula_11 and the probability density function of formula_11 with respect to the counting measure. We make this more precise below.  Suppose that formula_14 is a probability space and that formula_15 is a measurable space whose underlying σ-algebra is discrete, so in particular contains singleton sets of formula_16. In this setting, a random variable formula_17 is discrete provided its image is countable. The pushforward measure formula_18—called a distribution of formula_11 in this context—is a probability measure on formula_16 whose restriction to singleton sets induces a probability mass function formula_21 since formula_22 for each formula_23.  Now suppose that formula_24 is a measure space equipped with the counting measure μ. The probability density function formula_25 of formula_11 with respect to the counting measure, if it exists, is the Radon–Nikodym derivative of the pushforward measure of formula_11 (with respect to the counting measure), so formula_28 and formula_25 is a function from formula_16 to the non-negative reals. As a consequence, for any formula_23 we have  demonstrating that formula_25 is in fact a probability mass function.  When there is a natural order among the potential outcomes formula_10, it may be convenient to assign numerical values to them (or "n"-tuples in case of a discrete multivariate random variable) and to consider also values not in the image of formula_11. That is, formula_37 may be defined for all real numbers and formula_38 for all formula_39 as shown in the figure.  The image of formula_11 has a countable subset on which the probability mass function formula_41 is one. Consequently, the probability mass function is zero for all but a countable number of values of formula_10.  The discontinuity of probability mass functions is related to the fact that the cumulative distribution function of a discrete random variable is also discontinuous. If formula_11 is a discrete random variable, then formula_44 means that the casual event formula_45 is certain (it is true in the 100% of the occurrencies); on the contrary, formula_46 means that the casual event formula_45 is always impossible. This statement isn't true for a continuous random variable formula_11, for which formula_46 for any possible formula_10: in fact, by definition, a continuous random variable can have an infinite set of possible values and thus the probability it has a single particular value "x" is equal to formula_51. Discretization is the process of converting a continuous random variable into a discrete one.

Examples.

Finite.

There are three major distributions associated, the Bernoulli distribution, the Binomial distribution and the geometric distribution.  Other distributions that can be modeled using a probability mass function are the Categorical distribution (also known as the generalized Bernoulli distribution) and the multinomial distribution.

Multivariate case.

Two or more discrete random variables have a joint probability mass function, which gives the probability of each possible combination of realizations for the random variables.

In probability and statistics, a probability mass function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.

在概率论中,概率质量函数(probability mass function,简写为pmf)是离散随机变量在各特定取值上的概率。概率质量函数和概率密度函数不同之处在于:概率质量函数是对离散随机变量定义的,本身代表该值的概率;概率密度函数是对连续随机变量定义的,本身不是概率,只有对连续随机变量的概率密度函数在某区间内进行积分后才是概率。


Uses.

Microwaves are widely used for point-to-point communications because their small wavelength allows conveniently-sized antennas to direct them in narrow beams, which can be pointed directly at the receiving antenna. This allows nearby microwave equipment to use the same frequencies without interfering with each other, as lower frequency radio waves do. Another advantage is that the high frequency of microwaves gives the microwave band a very large information-carrying capacity; the microwave band has a bandwidth 30 times that of all the rest of the radio spectrum below it. A disadvantage is that microwaves are limited to line of sight propagation; they cannot pass around hills or mountains as lower frequency radio waves can. Microwave radio transmission is commonly used in point-to-point communication systems on the surface of the Earth, in satellite communications, and in deep space radio communications. Other parts of the microwave radio band are used for radars, radio navigation systems, sensor systems, and radio astronomy.  The next higher part of the radio electromagnetic spectrum, where the frequencies are above 30 GHz and below 100 GHz, are called "millimeter waves" because their wavelengths are conveniently measured in millimeters, and their wavelengths range from 10 mm down to 3.0 mm (Higher frequency waves are smaller in wavelength). Radio waves in this band are usually strongly attenuated by the Earthly atmosphere and particles contained in it, especially during wet weather. Also, in a wide band of frequencies around 60 GHz, the radio waves are strongly attenuated by molecular oxygen in the atmosphere. The electronic technologies needed in the millimeter wave band are also much more difficult to utilize than those of the microwave band.

Microwave radio relay.

Microwave radio relay is a technology widely used in the 1950s and 1960s for transmitting signals, such as long-distance telephone calls and television programs between two terrestrial points on a narrow beam of microwaves. In microwave radio relay, microwaves are transmitted on a line of sight path between relay stations using directional antennas, forming a fixed radio connection between the two points. The requirement of a line of sight limits the separation between stations to the visual horizon, about. Before the widespread use of communications satellites, chains of microwave relay stations were used to transmit telecommunication signals over transcontinental distances.  Beginning in the 1950s, networks of microwave relay links, such as the AT&T Long Lines system in the U.S., carried long distance telephone calls and television programs between cities. The first system, dubbed TD-2 and built by AT&T, connected New York and Boston in 1947 with a series of eight radio relay stations. These included long daisy-chained series of such links that traversed mountain ranges and spanned continents. Much of the transcontinental traffic is now carried by cheaper optical fibers and communication satellites, but microwave relay remains important for shorter distances.

Planning.

Because the radio waves travel in narrow beams confined to a line-of-sight path from one antenna to the other, they do not interfere with other microwave equipment, so nearby microwave links can use the same frequencies (see Frequency reuse). Antennas must be highly directional (high gain); these antennas are installed in elevated locations such as large radio towers in order to be able to transmit across long distances. Typical types of antenna used in radio relay link installations are parabolic antennas, dielectric lens, and horn-reflector antennas, which have a diameter of up to 4 meters. Highly directive antennas permit an economical use of the available frequency spectrum, despite long transmission distances.  Because of the high frequencies used, a line-of-sight path between the stations is required. Additionally, in order to avoid attenuation of the beam, an area around the beam called the first Fresnel zone must be free from obstacles. Obstacles in the signal field cause unwanted attenuation. High mountain peak or ridge positions are often ideal.  Obstacles, the curvature of the Earth, the geography of the area and reception issues arising from the use of nearby land (such as in manufacturing and forestry) are important issues to consider when planning radio links. In the planning process, it is essential that "path profiles" are produced, which provide information about the terrain and Fresnel zones affecting the transmission path. The presence of a water surface, such as a lake or river, along the path also must be taken into consideration since it can reflect the beam, and the direct and reflected beam can interfere at the receiving antenna, causing multipath fading. Multipath fades are usually deep only in a small spot and a narrow frequency band, so space and/or frequency diversity schemes can be applied to mitigate these effects.  The effects of atmospheric stratification cause the radio path to bend downward in a typical situation so a major distance is possible as the earth equivalent curvature increases from 6370 km to about 8500 km (a 4/3 equivalent radius effect). Rare events of temperature, humidity and pressure profile versus height, may produce large deviations and distortion of the propagation and affect transmission quality. High-intensity rain and snow making rain fade must also be considered as an impairment factor, especially at frequencies above 10 GHz. All previous factors, collectively known as path loss, make it necessary to compute suitable power margins, in order to maintain the link operative for a high percentage of time, like the standard 99.99% or 99.999% used in 'carrier class' services of most telecommunication operators.  The longest microwave radio relay known up to date crosses the Red Sea with a 360 km (200 mi) hop between Jebel Erba (2170m a.s.l.,, Sudan) and Jebel Dakka (2572m a.s.l.,, Saudi Arabia). The link was built in 1979 by to transmit 300 telephone channels and one TV signal, in the 2 GHz frequency band. (Hop distance is the distance between two microwave stations)  Previous considerations represent typical problems characterizing terrestrial radio links using microwaves for the so-called backbone networks: hop lengths of a few tens of kilometers (typically 10 to 60 km) were largely used until the 1990s. Frequency bands below 10 GHz, and above all, the information to be transmitted, were a stream containing a fixed capacity block. The target was to supply the requested availability for the whole block (Plesiochronous digital hierarchy, PDH, or Synchronous Digital Hierarchy, SDH). Fading and/or multipath affecting the link for short time period during the day had to be counteracted by the diversity architecture. During 1990s microwave radio links begun widely to be used for urban links in cellular network. Requirements regarding link distance changed to shorter hops (less than 10 km, typically 3 to 5 km), and frequency increased to bands between 11 and 43 GHz and more recently, up to 86 GHz (E-band). Furthermore, link planning deals more with intense rainfall and less with multipath, so diversity schemes became less used. Another big change that occurred during the last decade was an evolution toward packet radio transmission. Therefore, new countermeasures, such as adaptive modulation, have been adopted.  The emitted power is regulated for cellular and microwave systems. These microwave transmissions use emitted power typically from 0.03 to 0.30 W, radiated by a parabolic antenna on a narrow beam diverging by a few degrees (1 to 3-4). The microwave channel arrangement is regulated by International Telecommunication Union (ITU-R) and local regulations (ETSI, FCC). In the last decade the dedicated spectrum for each microwave band has become extremely crowded, motivating the use of techniques to increase transmission capacity such as frequency reuse, Polarization-division multiplexing, XPIC, MIMO.

History.

The history of radio relay communication began in 1898 from the publication by Johann Mattausch in Austrian journal, Zeitschrift für Electrotechnik. But his proposal was primitive and not suitable for practical use. The first experiments with radio repeater stations to relay radio signals were done in 1899 by Emile Guarini-Foresio. However the low frequency and medium frequency radio waves used during the first 40 years of radio proved to be able to travel long distances by ground wave and skywave propagation. The need for radio relay did not really begin until the 1940s exploitation of microwaves, which traveled by line of sight and so were limited to a propagation distance of about by the visual horizon. In 1931 an Anglo-French consortium headed by Andre C. Clavier demonstrated an experimental microwave relay link across the English Channel using dishes. Telephony, telegraph, and facsimile data was transmitted over the bidirectional 1.7 GHz beams between Dover, UK, and Calais, France. The radiated power, produced by a miniature Barkhausen-Kurz tube located at the dish's focus, was one-half watt. A 1933 military microwave link between airports at St. Inglevert, France, and Lympne, UK, a distance of, was followed in 1935 by a 300 MHz telecommunication link, the first commercial microwave relay system.  The development of radar during World War II provided much of the microwave technology which made practical microwave communication links possible, particularly the klystron oscillator and techniques of designing parabolic antennas. Though not commonly known, the US military used both portable and fixed-station microwave communications in the European Theater during World War II.  After the war, telephone companies used this technology to build large microwave radio relay networks to carry long distance telephone calls. During the 1950s a unit of the US telephone carrier, AT&T Long Lines, built a transcontinental system of microwave relay links across the US that grew to carry the majority of US long distance telephone traffic, as well as television network signals. The main motivation in 1946 to use microwave radio instead of cable was that a large capacity could be installed quickly and at less cost. It was expected at that time that the annual operating costs for microwave radio would be greater than for cable. There were two main reasons that a large capacity had to be introduced suddenly: Pent up demand for long distance telephone service, because of the hiatus during the war years, and the new medium of television, which needed more bandwidth than radio. The prototype was called TDX and was tested with a connection between New York City and Murray Hill, the location of Bell Laboratories in 1946. The TDX system was set up between New York and Boston in 1947. The TDX was upgraded to the TD2 system, which used [the Morton tube, 416B and later 416C, manufactured by Western Electric] in the transmitters, and then later to TD3 that used solid state electronics. Remarkable were the microwave relay links to West Berlin during the Cold War, which had to be built and operated due to the large distance between West-Germany and Berlin at the edge of the technical feasibility. In addition to the telephone network, also microwave relay links for the distribution of TV & Radio broadcasting programs. This included connections from the studios to the broadcasting systems distributed across the country, as well as between the radio stations, for example for program exchange.  Military microwave relay systems continued to be used into the 1960s, when many of these systems were supplanted with tropospheric scatter or communication satellite systems. When the NATO military arm was formed, much of this existing equipment was transferred to communications groups. The typical communications systems used by NATO during that time period consisted of the technologies which had been developed for use by the telephone carrier entities in host countries. One example from the USA is the RCA CW-20A 1–2 GHz microwave relay system which utilized flexible UHF cable rather than the rigid waveguide required by higher frequency systems, making it ideal for tactical applications. The typical microwave relay installation or portable van had two radio systems (plus backup) connecting two line of sight sites. These radios would often carry 24 telephone channels frequency division multiplexed on the microwave carrier (i.e. Lenkurt 33C FDM). Any channel could be designated to carry up to 18 teletype communications instead. Similar systems from Germany and other member nations were also in use.  Long-distance microwave relay networks were built in many countries until the 1980s, when the technology lost its share of fixed operation to newer technologies such as fiber-optic cable and communication satellites, which offer a lower cost per bit. During the Cold War, the US intelligence agencies, such as the National Security Agency (NSA), were reportedly able to intercept Soviet microwave traffic using satellites such as Rhyolite. Much of the beam of a microwave link passes the receiving antenna and radiates toward the horizon, into space. By positioning a geosynchronous satellite in the path of the beam, the microwave beam can be received.  At the turn of the century, microwave radio relay systems are being used increasingly in portable radio applications. The technology is particularly suited to this application because of lower operating costs, a more efficient infrastructure, and provision of direct hardware access to the portable radio operator.

Microwave link.

A microwave link is a communications system that uses a beam of radio waves in the microwave frequency range to transmit video, audio, or data between two locations, which can be from just a few feet or meters to several miles or kilometers apart. Microwave links are commonly used by television broadcasters to transmit programmes across a country, for instance, or from an outside broadcast back to a studio.  Mobile units can be camera mounted, allowing cameras the freedom to move around without trailing cables. These are often seen on the touchlines of sports fields on Steadicam systems.

Troposcatter.

Terrestrial microwave relay links are limited in distance to the visual horizon, a few tens of miles or kilometers depending on tower height. Tropospheric scatter ("troposcatter" or "scatter") was a technology developed in the 1950s to allow microwave communication links beyond the horizon, to a range of several hundred kilometers. The transmitter radiates a beam of microwaves into the sky, at a shallow angle above the horizon toward the receiver. As the beam passes through the troposphere a small fraction of the microwave energy is scattered back toward the ground by water vapor and dust in the air. A sensitive receiver beyond the horizon picks up this reflected signal. Signal clarity obtained by this method depends on the weather and other factors, and as a result a high level of technical difficulty is involved in the creation of a reliable over horizon radio relay link. Troposcatter links are therefore only used in special circumstances where satellites and other long distance communication channels cannot be relied on, such as in military communications.

Microwave transmission is the transmission of information by microwave radio waves. Although an experimental microwave telecommunication link across the English Channel was demonstrated in 1931, the development of radar in World War II provided the technology for practical exploitation of microwave communication. In the 1950s, large transcontinental "microwave relay" networks, consisting of chains of repeater stations linked by line-of-sight beams of microwaves were built in Europe and America to relay long distance telephone traffic and television programs between cities. Communication satellites which transferred data between ground stations by microwaves took over much long distance traffic in the 1960s. In recent years, there has been an explosive increase in use of the microwave spectrum by new telecommunication technologies such as wireless networks, and direct-broadcast satellites which broadcast television and radio directly into consumers' homes.

微波通讯是指一种综合技术,将信号以频率在0.3 GHz 至300 GHz的微波作为载体传输。 部分被称作毫米波的微波辐射非常容易被大气层(特别是潮湿的天气)衰减。