In mathematics, the universality of zeta-functions is the remarkable ability of the Riemann zeta-function and other, similar, functions, such as the Dirichlet L-functions, to approximate arbitrary non-vanishing holomorphic functions arbitrarily well.

A mathematically precise statement of universality for the Riemann zeta-function ζ ( s ) follows.

Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.

; Unrestricted domain: ( or universality ) For any set of individual voter preferences, the social welfare function should yield a unique and complete ranking of societal choices.

There, it was first clearly shown that mean field theory approaches failed to predict the correct behavior at the critical point ( which was found to fall under a universality class that includes many other systems, such as liquid-gas transitions ), and had to be replaced by renormalization group theory.

The feeling in 1848 was far inferior to this in strength and universality.

This emphasis, on languages other than Romance languages, also had the effect of reducing the universality of his translated works and original academic writings, as Latin was the lingua franca in both Iberia and Europe ; yet Alfonso never desisted in his promotion of the Castilian vernacular.

Feuerbach goes on to postulate that the emergence of monotheism and thus the end of the Pagan period was a development which naturally grew out of Hellenistic philosophy due to the contradiction inherent in the ethnic nature of Pagan tradition and the universality of human spirituality ( Geist ), finally resulting in the emergence of a religion with a universalist scope in the form of Christianity.

According to FISA, this weight category was introduced " to encourage more universality in the sport especially among nations with less statuesque people ".

Franklin's cultural relativism was perhaps one of the purest expressions of Enlightenment assumptions that stressed racial equality and the universality of moral sense among peoples.

Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.

Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.

In 1980, Baez was given honorary Doctor of Humane Letters degrees by Antioch University and Rutgers University for her political activism and the " universality of her music ".

Between World War I and World War II, " cultural relativism " was the central tool for American anthropologists in this refusal of Western claims to universality, and salvage of non-Western cultures.

The idea was that the government and the central bank would maintain rough full employment, so that neoclassical notions — centered on the axiom of the universality of scarcity — would apply.

He was a symbol to European Christians of the Church's universality, transcending culture and geography to encompass all humanity, in a time when ethnic and inter-religious tension made such a vision seem distant.

In 2007, as part of commemorating the fifth anniversary of the book, a $ 25, 000 prize was offered for a proof of the ( 2, 3 ) machine's universality .< ref >

The universality of Langton's ant was proven in 2000.

According to the Israel Ministry of Foreign Affairs, Magen David Adom was boycotted by the International Committee of the Red Cross, which refused to grant the organization membership because " it was … argued that having an emblem used by only one country was contrary to the principles of universality.

" The minutes of the AAAS meeting reveal that because of the universality of this " view on the subject, it was suggested whether the states of Christendom might not be induced to cooperate with their Navies in the undertaking ; at least so far as to cause abstracts of their log-books and sea journals to be furnished to Matthew F. Maury, USN, at the Naval Observatory at Washington.

Denis Lemon, the editor and owner of Gay News, had published the poem on the basis that the " message and intention of the poem was to celebrate the absolute universality of God's love.

Spencer's interest in psychology derived from a more fundamental concern which was to establish the universality of natural law.

Comte's Système de Philosophie Positive had been written with the ambition of demonstrating the universality of natural law, and Spencer was to follow Comte in the scale of his ambition.

' Like Comte, he was committed to the universality of natural law, the idea that the laws of nature applied without exception, to the organic realm as much as to the inorganic, and to the human mind as much as to the rest of creation.

This was called universality and is successfully explained by RG, just

By the ending of Modern Times, “ the film seems tailored to please the middle-class optimist .” Due to all of their failings the final scene had the gamine stating, “ What's the use of trying ?”, with the Tramp replying with, “ Buck up – never say die .” Chaplin was unique among the silent film comedians because of his physical shtick, but also because of the universality of his class struggle humor and his social commentary.

It is only within the framework of this universality that we can understand the preference, that is, ' what comes first.

The universality of Sirius lore, even the Pawnee tribe of North America, and others, referred to Sirius as the ' Wolf Star ', indicates this Sothic Mythos may have extremely ancient roots, perhaps as old as the first humans to migrate from Africa.

The stages ( moments ) of the Concept in Hegel's triad are the universal, the particular, and the individual: universality develops, first into particularity, and then into individuality.

His first book summarizes his previous work and organizes his ideas of unity and universality of physical laws, making his works accessible to other scientists.

< li > Mixed Blood presented with Actors ’ Equity Association ’ s first Rosetta LeNoire Award for “ celebrating the universality of the human experience on the American stage ”</ li >

Christian writings from the second, third and fourth centuries AD testify to the universality of the moral influence view among Christians during that the first few centuries AD ( see above ).

Like other concepts from statistical mechanics ( such as entropy and master equations ), universality has proven a useful construct for characterizing distributed systems at a higher level, such as multi-agent systems.

Inspired by the Black Death, The Dance of Death, an allegory on the universality of death, is a common painting motif in the late medieval period.

The universality of this code is generally regarded by biologists as definitive evidence in favor of the theory of universal common descent.

Christianity is characterized by its claim to universality, which marks a significant break from current Jewish identity and thought, but has its roots in Hellenistic Judaism.

In other words, the general problem of Diophantine analysis is blessed or cursed with universality, and in any case is not something that will be solved except by re-expressing it in other terms.

According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors ( see Eötvös experiment ), there is a universality of free fall ( also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass ): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.

Although the bending of light can also be derived by extending the universality of free fall to light, the angle of deflection resulting from such calculations is only half the value given by general relativity.

The strong claims made by human rights to universality have led to persistent criticism.

On the basis of universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces.

However, he believed that ' a painter must be part of the land and of the life he paints ', and his own artistic development, as a Modernist and Expressionist, helped articulate a modern Dublin of the 20th century, partly by depicting specifically Irish subjects, but also by doing so in the light of universal themes such as the loneliness of the individual, and the universality of the plight of man.

A more modern response to this criticism of concepts without sense-perception is the claim that the universality of its qualities is an unavoidable given because one only experiences an object by means of general concepts.

In fact, almost all material phase transitions are described by a small set of universality classes.

However, they believe such necessary universality can and should be achieved by developing a richer notion of morality through reason, experience and scientific inquiry rather than through faith in a supernatural realm or source.

The term " weakly universal " is sometimes used to distinguish a system ( e. g. a cellular automaton ) whose universality is achieved only by modifying the standard definition of Turing machine so as to include input streams with infinitely many 1s.

The former view is the one adopted by Bentham and Mill, and ( I believe ) by the Utilitarian school generally: and is obviously most in accordance with the universality that is characteristic of their principle ... it seems arbitrary and unreasonable to exclude from the end, as so conceived, any pleasure of any sentient being.

Legend is distinguished from the genre of chronicle by the fact that legends apply structures that reveal a moral definition to events, providing meaning that lifts them above the repetitions and constraints of average human lives and giving them a universality that makes them worth repeating through many generations.

In The Society of the Spectacle, Debord asserted ideology is " the abstract will to universality and the illusion thereof ," which is " legitimated in modern society by universal abstraction and by the effective dictatorship of illusion.

Further Dawkins distinguishes this process from the spread of scientific ideas, which, he suggests, is constrained by the requirement to conform with certain virtues of standard methodology: " testability, evidential support, precision, quantifiability, consistency, intersubjectivity, repeatability, universality, progressiveness, independence of cultural milieu, and so on ".

The problem of computational universality is solved in this case by keeping predefined jump tables in the memory.

Van Valin also departs from Chomskyan syntactic theory by denying the universality of the verb phrase.