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hypothesis and ƒ
Let ƒ and g be two functions satisfying the above hypothesis that ƒ is continuous on I and is continuous on the closed interval.

hypothesis and obey
* Friedmann-Lemaître-Robertson-Walker for the best known cosmological model ( which does obey Weyl's hypothesis )
Just as the Riemann zeta function is conjectured to obey the Riemann hypothesis, so the Dirichlet L-functions are conjectured to obey the generalized Riemann hypothesis.

hypothesis and Cauchy
In 1832, by the aid of a particular hypothesis as to the constitution of the ether, he reached by a rigorous dynamical calculation results agreeing with those obtained by Augustin Louis Cauchy, and succeeded in deducing laws of double refraction closely resembling those of Augustin-Jean Fresnel.
They believe that quantum wave-functions do not collapse like the Copenhagen interpretation holds, nor that each collapse actually buds off separate universes ( like the quantum multiverse hypothesis holds ) but rather that the universe is a participatory universe: the entire universe exists as a single massive quantum superposition, and that at the end of time ( in the open universe of the Xeelee Sequence, time and space are unbounded, or more precisely, bounded only at the Cauchy boundaries of " Time-like infinity " and " Space-like infinity "), when intelligent life has collected all information ( compare the Final anthropic principle and the Omega Point ), and transformed into an " Ultimate Observer ", who will make the " Final observation ", the observation which collapses all the possible entangled wave-functions generated since the beginning of the universe.

hypothesis and
While the Ural Altaic hypothesis can still be found in encyclopedias, atlases, and similar general references, it has not had any adherents in the linguistics community for decades.
He rejected the Ural Altaic hypothesis, included Korean in Altaic, an inclusion followed by most leading Altaicists to date.
This hypothesis of the contents of the Mouseion, originally suggested by Nietzsche ( Rheinisches Museum 25 ( 1870 ) & 28 ( 1873 )), appears to have been confirmed by three papyrus finds one 3rd century BC ( Flinders Petrie Papyri, ed.
* Abortion breast cancer hypothesis, a posited connection between breast cancer and abortion
This principle has frequently been called the " Sapir Whorf hypothesis ", after him and his mentor Edward Sapir, but Whorf called it the principle of linguistic relativity, because he saw the idea as having implications similar to Einstein's principle of physical relativity.
This debate is analogous to that surrounding the Sapir Whorf hypothesis in linguistics and cognitive science, which postulates that a particular spoken language's nature influences the habitual thought of its speakers.
The outcome of a cladistic analysis is a cladogram a tree-shaped diagram ( dendrogram ) that represents a phylogenetic hypothesis, a hypothesis on evolutionary relationships.
The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.
More specifically, the continuum hypothesis / assumption hinges on the concepts of a representative volume element ( RVE ) ( sometimes called " representative elementary volume ") and separation of scales based on the Hill Mandel condition.
Wegener was the first to use the phrase " continental drift " ( 1912, 1915 ) ( in German " die Verschiebung der Kontinente " translated into English in 1922 ) and formally publish the hypothesis that the continents had somehow " drifted " apart.
In computability theory, the Church Turing thesis ( also known as the Turing-Church thesis, the Church Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.
A reviewer concluded that Stickel brought forward every possible argument which would speak for that hypothesis, but he proved the opposite of what he had attempted to do ( Johannes Gildemeister in ZDMG 13, 1859, 289 304 ).
The hypothesis is that the gravitational interaction is likewise mediated by a yet undiscovered elementary particle, dubbed the graviton.
In China, the polymath Shen Kuo ( 1031 1095 ) formulated a hypothesis for the process of land formation: based on his observation of fossil animal shells in a geological stratum in a mountain hundreds of miles from the ocean, he inferred that the land was formed by erosion of the mountains and by deposition of silt.
While the Trivers Willard hypothesis predicts that birth sex is dependent on living conditions ( i. e. more male children are born in " good " living conditions, while more female children are born in poorer living conditions ), the probability of having a child of either gender is still regarded as 50 / 50.
Both the form of the Kolmogorov Smirnov test statistic and its asymptotic distribution under the null hypothesis were published by Andrey Kolmogorov, while a table of the distribution was published by Nikolai Vasilyevich Smirnov.
* Sapir Whorf hypothesis
This too was shown to be incorrect by the Michelson Gale Pearson experiment, which detected the Sagnac effect due to Earth's rotation ( s. Aether drag hypothesis )
The fact that ten vowels have been reconstructed for proto-Atlantic, proto-Ijoid and possibly proto-Volta Congo leads Williamson ( 1989: 23 ) to the hypothesis that the original vowel inventory of Niger Congo was a full ten-vowel system.

hypothesis and Riemann
Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems.
Among his major accomplishments were the 1940 proof, of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result ( from 1942 to 1946, most intensively ).
* The Riemann hypothesis
For example, the Riemann hypothesis is a conjecture from number theory that ( amongst other things ) makes predictions about the distribution of prime numbers.
Few number theorists doubt that the Riemann hypothesis is true ( it is said that Atle Selberg was once a sceptic, and J. E. Littlewood always was ).
Likewise, the Riemann hypothesis has a large number of consequences already proven.
Of the initial twenty-three Hilbert problems, most of which have been solved, only the Riemann hypothesis ( formulated in 1859 ) is included in the seven Millennium Prize Problems.
* The Riemann hypothesis
This result can sometimes substitute for the still-unproved generalized Riemann hypothesis.
# REDIRECT Riemann hypothesis
( Indeed, the behavior of this difference is very complicated and related to the Riemann hypothesis.
Because of the connection between the Riemann zeta function and π ( x ), 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 and only if the Riemann hypothesis is true, the error term in the above relation can be improved to
The constant involved in the big O notation was estimated in 1976 by Lowell Schoenfeld: assuming the Riemann hypothesis,
Under the assumption of the generalized Riemann hypothesis, it can be shown to take time
Under the Riemann hypothesis, the error term can be reduced:
The Riemann hypothesis has been verified for the first 10 trillion zeroes of the zeta function.
Other famous conjectures include the Collatz conjecture and the Riemann hypothesis.
* Riemann hypothesis and the generalized Riemann hypothesis.
* Bernhard Riemann formulates the Riemann hypothesis, one of the most important open problems of contemporary mathematics.

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