Displaying similar documents to “Expressing f ∈ 𝒟 as a difference of two positive functions f 1 , f 2 ∈ 𝒟 ”

On integer stochastic approximation

Václav Dupač, Ulrich Herkenrath (1984)

Aplikace matematiky

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Let M : 𝐑 → 𝐑 be observable, with experimental errors, at integer points only; unknown elsewhere. Iterative nonparametric procedures for finding the zero point of M are called procedures of integer stochastic approximation. Three types of such procedures (Derman’s, Mukerjee’s and the authors’) are described and compared. A two-dimensional analogue of the third approach is proposed and investigated; its generalization to higher dimensions is conjectured.

On periodic solution of a nonlinear beam equation

Marie Kopáčková (1983)

Aplikace matematiky

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the existence of an ω -periodic solution of the equation ∂ 2 u ∂ t 2 + α ∂ 4 u ∂ x 4 + γ ∂ 5 u ∂ x 4 ∂ t - γ ˜ ∂ 3 u ∂ x 2 ∂ t + δ ∂ u ∂ t - β + ℵ ∫ 0 n ∂ u ∂ x 2 ( · , ξ ) d ξ + σ ∫ 0 n ∂ 2 u ∂ x ∂ t ( · , ξ ) ∂ u ∂ x ( · , ξ ) d ξ ∂ 2 u ∂ x 2 = f sarisfying the boundary conditions u ( t , 0 ) = u ( t , π ) = ∂ 2 u ∂ x 2 t , 0 = ∂ 2 u ∂ x 2 t , π = 0 is proved for every ω -periodic function f ∈ C 0 , ω , L 2 .