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 function of For instance, we find that |f(u)| ≤ L(u) + O(ε2/3), where L(u) is the Boas-Kac-Lukosz bound, and show by means of an example that this version is the sharpest possible with respect to its behaviour as a function of ε as ε ↓ 0. We prove a Tauberian theorem of the form $\phi * g (x)\sim p(x)w(x)$ as $x \to \infty,$ where p(x) is a bounded periodic function and w(x) is a weighted function of power growth. When F is the characteristic function of [0, R2], this gives a representation for radial Fourier inversion. In this article we develop the theory of one-sided versions of the g function of Littlewood and Paley, the area function S of Lusin and the that admit weighted norm estimates with weights belonging to the classes Ap+ of Sawyer. The function, is a characteristic function of a probability distribution iff. This criterion implies several results concerning the problem of integrable solutions of n-scale refinement equations and the problem of absolutely continuity of distribution function of one random series. Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. We also provide two sufficient and verifiable conditions for a nondecreasing function to be the spectral function of a singular Sturm Liouville operator. This paper provides a functional equation satisfied by the dichromatic sum function of rooted outer-planar maps. Influence function of correlation of several random vectors with its applications Influence function of a statistic describes the effect of a small perturbation of the data on this statistic. The value function of the original fast problem converges locally uniformly to the value function of the averaged problem under both cases. The paper is concerned with the filled functions for global optimization of a continuous function of several variables. This article deals with the reflective function of the mth-order nonlinear differential systems. The nonlinear differential equation * is considered, where δ(t) is a periodic function of periodic T, f(t,x) is continuous and periodic in t. The conclusion that the equilibrium is the continuous function of the dilution rate and substrate concentration in medium in a certain range is concluded. Expected discounted penalty function of erlang(2) risk model with constant interest This article deals with the reflecting function of the differential systems. Based on the mass spectra search function of GC/qMS with the aid of the discriminability of the geometrical isomer by GC/FTIR and the ability to determine the accurate mass charge ratio (m/z) by GC/oaTOFMS, 68 GC eluants were identified successfully. Studies on CMC and thermodynamic function of anionic surfactants in DMA/long-chain alcohol systems using microcalorimetric metho

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