During the past decade there have been many changes in the perfumery industry which are not so much due to the discovery and application of new raw materials, but rather to the astronomic increase in the cost of labour required to produce them. This is reflected more particularly in the flower industry, where the cost of collecting the blossoms delivered to the factories has gone up year after year, so much so that most flowers with the possible exception of Mimosa, have reached a cost price which has compelled the perfumer to either reduce his purchases of absolutes and concretes, or alternatively to substitute them from a cheaper source, or even to discontinue their use. This development raises an important and almost insoluble problem for the perfumer, who is faced with the necessity of trying to keep unchanged the bouquet of his fragrances, and moreover, to ensure no loss of strength and diffusiveness. Of course, this problem applies more especially to the adjustment of formulae for established perfumes, because in every new creation the present high cost of raw materials receives imperative con- sideration before the formula is approved.
In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations.
In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied.
This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.
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