Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page

Six Sigma as a Business Process Management Method in Services: Analysis of the Key Application Problems

Apart from being applied in production, Six Sigma has grown considerably in importance as a business process management (BPM) method in services. The transfer of the method from production to service applications does, however, pose problems which affect the success of implementing Six Sigma as a BPM method in services. For a successful application of the Six Sigma method in services it is helpful to know these possible problems in order to be able to avoid them and to achieve the goals of Six Sigma improvement projects. In addition from a theoretical view knowing the problems is a first step for further development of the Six Sigma method. Therefore, the present article deals with the following questions: which key problems regarding the application of Six Sigma in services are mentioned in the literature and which phases of the Six Sigma cycle can they be assigned to? The existing literature on this subject is reviewed and a qualitative content analysis of its contents is presented. Additionally, a survey based on the problems found in the literature is conducted to compare theory and practice. The evaluation of the results shows, on the one hand, that to date the problems of the application of Six Sigma in services have little been dealt with. On the other hand the evaluation provides a survey of the problems structured in accordance to the phases of the Six Sigma cycle. Thus, the present paper offers new findings as regards the state-of-the-art of the Six Sigma method