An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

Research technique and test experiments for the analysis of petrophysical properties of weak-consolidated and friable rocks

With the use of created measuring system for the study of petrophysical properties of incompetent, friable and loose rocks and sludge samples test experiments were performed on pit sand samples of known grain-size distribution, consolidated and disintegrated rock samples of Subbotin oil field of the Maykop formation. It was experimentally established that the shrinkage rate of soft rocks decreases sharply and attenuates at the effective pressure of 30 to 35MPa, which leads to stabilization of their filtration-capacitive and deformation behavior. The research of rocks, which are returned during drilling in the form of sand and cuttings, opens opportunities for using the obtained data for interpretation of production well logging and calculation of hydrocarbon reserves

Repulsive Casimir Force: Sufficient Conditions

In this paper the Casimir energy of two parallel plates made by materials of different penetration depth and no medium in between is derived. We study the Casimir force density and derive analytical constraints on the two penetration depths which are sufficient conditions to ensure repulsion. Compared to other methods our approach needs no specific model for dielectric or magnetic material properties and constitutes a complementary analysis.Comment: 11 pages. 3 figures. Misprints corrected in Eq. (4

The Scientific-Practical Approach to Development of Economic-Organizational Provision of the Logistic Activity of Enterprise

The article is aimed at forming a scientific-practical approach to the development of economic-organizational provision of logistic activity of enterprise in modern economic conditions. Approaches to definition of the logistic activity of enterprise are allocated. It is determined that the important provisions of logistics management are not only logistical concepts, but also logistical approaches, in particular: system, functional, and process. The bases of formation of the logistic activity of enterprises are analyzed. On the basis of the conducted research the scientific-practical approach to development of economic-organizational provision of the logistic activity of enterprise is formed, essence of which consists in combination of interests of producer, consumer and supplier, with attention to the economic and organizational support. This approach includes the purpose, tasks, functions and principles, use of the methodical instrumentarium, carrying out of complex analysis of the activity of enterprise, formation and introduction of the efficient managerial decisions concerning the logistic activity of enterprise

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