Displaying similar documents to “On the problem of Gauss”

«Approximate approximations» and the cubature of potentials

Gunther Schmidt (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

The paper discusses new cubature formulas for classical integral operators of mathematical physics based on the «approximate approximation» of the density with Gaussian and related functions. We derive formulas for the cubature of harmonic, elastic and diffraction potentials approximating with high order in some range relevant for numerical computations. We prove error estimates and provide numerical results for the Newton potential.

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

Similarity:

Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.

Statistical choice of non-separated one-parameter models.

José Tiago de Oliveira (1985)

Trabajos de Estadística e Investigación Operativa

Similarity:

The purpose of this paper is to study the asymptotic choice between two models {F(x|α), α ∈ A ⊆ R} and {G(x|β), β ∈ B ⊆ R}, A and B being intervals but such that for (α, β}, and only for this pair, we have F(x|α) = G(x|β).