均匀分布可以生成其他所有分布,相反地,从任一分布可以生成均匀分布。 为了简单起见,假设分布的CDF为严格单调增函数,确保逆函数存在: 根据之前的假设,分布的CDF为严格单调增函数,故根据函数的单调性: F(-1)(U)<=x可以得到F[F(-1)(U)]<=F(x),因此可以证明: ...
uniform distribution modulo 1In the paper, we prove a joint universality theorem on the approximation of a collection of analytic functions by a collection of shifts of Dirichlet L-functions L(s + iτ,(Formula presented.)j), where (Formula presented.) takes values from the set {kα: k =...
Related to Universality of free fall:Weak equivalence principle equivalence principle (i-kwiv-ă-lĕns)The principle that, on a local scale, the physical effects of a uniform acceleration of someframe of referenceimitates completely the behavior in a uniform gravitational field. This equivalence of...
We would like to emphasize that, our analysis will be based on stellar interiors with non-uniform density distribution, so that the velocity of sound remains less than that of light, as well as the pressure remains positive and finite at the centre of the stellar structure, even when the ...
In 1929 Birkhoff [7] proved the universality of translation operators on H(C) endowed with the topology of uniform convergence on compact sets. Godefroy and Shapiro [19] showed that every operator on H(CN) that commutes with all translations, and is not a scalar multiple of the identity, ...
We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ ( s + i γ k ), k ∈ ℕ, of the Riemann zeta-function, where γ k are imaginary parts of nontrivial zeros of ζ ( s ).
Introducing easy-plane exchange anisotropy leaves the critical point of the S = 1/2 system unchanged and changes the critical exponents [4], whereas the critical bond alternation of the S = 1 system is altered. Furthermore, the universality classes become different. Numerical analysis of the ...
If we converge to the stationary solution in a uniform fashion, then the we need ɛO1ɛ amount of time during which the error becomes ɛɛo1ɛ⋅ɛ=o(1). Note that this argument implicitly assumes that the linearization breaks down only after the largest eigenvector starts ...
A hypothesis that packing fraction alone can be used to characterize the structure of a sphere packing, known as the quasi-universality in the literature, is tested. The analysis, conducted in terms of coordination number, radial distribution function, and structural properties from the Voronoi/Delau...
Mergelyan, S.N.: Uniform approximations to functions of a complex variable. Uspekhi Mat. Nauk 7(2), 31–122 (1952). (in Russian) MathSciNet MATH Google Scholar Mishou, H.: The joint value distribution of the Riemann zeta-function and Hurwitz zeta-functions. Lith. Math. J. 47, 32...