| 释义 |
Riemann Math.|ˈriːmən|
The name of G. F. Bernhard Riemann (1826–66), German mathematician, used attrib. and in the possessive to designate various concepts of his, as Riemann geometry, Riemannian geometry; Riemann('s) hypothesis, the hypothesis (unproved by 1981) that all the zeros of the Riemann zeta function, except those on the real line, have a real part equal to ½; Riemann integral, a definite integral obtained by subdividing the interval of integration, multiplying the width of each subdivision by the greatest or the least value of the integrand within it, summing the products so obtained, and taking the limit of the sum as the width of the subdivisions tends to zero; so Riemann integrable adj. phr., Riemann integration; Riemann('s) surface, a surface which covers a plane more than once, and so could be used to plot a function that is not single-valued; Riemann tensor, the Riemann–Christoffel tensor; Riemann zeta (or ζ) function, an analytic function ζ of the complex variable s, equal almost everywhere to {ob}1-s + 2-s + 3-s +{ddd}{cb}.
1922Proc. Nat. Acad. Sci. VIII. 23 The functions λgij satisfy (2.4) and give a Riemann geometry. 1974R. M. Pirsig Zen & Art of Motorcycle Maintenance (1976) iii. xxii. 257 He turned to the question, Is Euclidian geometry true or is Riemann geometry true? He answered, The question has no meaning.
1924Proc. Cambr. Philos. Soc. XXII. 296 We assume Riemann's hypothesis. Ibid., We assume the truth of the Riemann hypothesis. 1959Listener 23 Apr. 715/2 This conjecture, now known as the Riemann hypothesis, has never been either proved or disproved.
1957K. S. Miller Advanced Real Calculus iv. 49 If I′ = I{pp} we shall say that f(x) is Riemann integrable or simply integrable on [a,b] and write I = ∫ba f(x)dx . 1972A. G. Howson Handbk. Terms Algebra & Anal. xxvii. 136 If f is bounded on I then it is Riemann integrable..on I if and only if it is continuous almost everywhere..on I.
1914Proc. London Math. Soc. XIII. 133 Corresponding to Riemann's extension of the notion of an integrable function, we now have a certain class of functions which may be said to possess a ‘Riemann’ integral with respect to the monotone increasing function g(x), that is to say a function such that the summation..has a unique and finite limit, however the points x are chosen in their corresponding intervals, and however those intervals are constructed, provided only the length of the greatest of them approaches zero as n → ∞. 1970S. Kotz tr. Pesin's Classical & Mod. Integration Theories vii. 112 The Riemann integral can be defined in two ways: by the Riemann process as the limit of Riemann's sums and by the Darboux process as the common value of the lower and upper integrals.
1939I. S. Sokolnikoff Advanced Calculus iv. 99 It seems desirable to begin the study of Riemann integration by presenting a reasonably careful definition of the definite integral based on the intuitive concept of the area under the curve.
1893A. R. Forsyth Theory Functions Complex Variable xv. 336 The region, in which the variable z exists, no longer consists of a single plane but of a number of planes.., often called sheets... The aggregate of all the sheets is a surface, often called a Riemann's Surface. 1893Harkness & Morley Treat. Theory Functions vi. 205 We shall show how to form a Riemann surface in some simple special cases. 1932A. Huxley Brave New World iv. 73 Two thousand Beta-Minus mixed doubles were playing Riemann-surface tennis. 1974Encycl. Brit. Macropædia I. 726/2 A compact Riemann surface is homeomorphic to the (topological) surface obtained from a sphere by cutting g pairs of holes in it and attaching to each pair of holes a handle.
1922Proc. Nat. Acad. Sci. VIII. 24 Where Rpq,rs is the Riemann tensor of the first kind. 1957Physical Rev. CV. 1089/1 It is the Riemann tensor which characterizes the presence of radiation. Physically, this is because the Riemann tensor describes the variations in the gravitational field from event to event in space-time. 1973Hawking & Ellis Large Scale Structure of Space–Time ii. 42 Having split the Riemann tensor into a part represented by the Ricci tensor and a part represented by the Weyl tensor, one can use the Bianchi identities..to obtain differential relations between the Ricci tensor and the Weyl tensor.
1899Messenger of Math. XXIX. 114 If ζ(s, a, ω) be the extended Riemann ζ function. 1931Q. Jrnl. Math. II. 161 The theory of the Riemann zeta-function. 1966Ogilvy & Anderson Excursions in Number Theory iii. 35 We needed a value of the Riemann Zeta-function, the technical name for the series that converged to π2/6. |
