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In this work the behavior of power corrections to Adler function in operator product expansion (OPE) is studied, in particular the possible contribution of operator of dimension 2. The OPE terms of dimension 4 and 6 are taken into account. Various experimental data on reactions of e+e--annihilation to pion channels (π+π-, 2π+2π-, π+π-2π0, 3π+3π-, 2π+2π-2π0) are used. The high-precision fits of the experimental data are obtained and used. The method based on Borel transformation of Adler function is applied. It is shown that the contribution of operator of dimension 2 is negative being compatible to zero at three standard deviations level. The strong (anti)correlation between short string and local gluon condensate is found. [ABSTRACT FROM AUTHOR]

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Lebesgue measure on Rn is restriction of outer Lebesgue measure to the family of Lebesgue measurable sets. All properties of Lebesgue positive measure on R are transferred to Lebesgue measure on Rn. The Lebesgue measure on B is only meassure defined on σ-algebra of Borel sets of Rn, which is invariance to translation and √(I) = 1, for I= [0,1] × [0,1] × ... × [0,1]./n times [ABSTRACT FROM AUTHOR]

It is well known that the notion of measure and integral were released early enough in close connection with practical problems of measuring of geometric figures. Notion of measure was outlined in the early 20th century through H. Lebesgue's research, founder of the modern theory of measure and integral. It was developed concurrently a technique of integration of functions. Gradually it was formed a specific area today called the measure and integral theory. Essential contributions to building this theory were made by a large number of mathematicians: C. Carathodory, J. Radon, O. Nikodym, S. Bochner, J. Pettis, P. Halmos and many others. In the following we present several abstract sets, classes of sets, positive measure on a σ-algebra, Lebesgue measure on R and the particularly measure Lebesgue-Stieltjes measure on R. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the behavior of the interpolating points of maximally convergent multipoint Padé approximants with fixed degree of the denominators. [ABSTRACT FROM AUTHOR]

Necessary conditions in an optimization problem for differential inclusions with convex right-hand side are given. The initial state of the inclusion being a random vector is unknown, or, in the more general case, is contained in some random closed set. We seek a trajectory of the inclusion which minimizes the expectation of a function of the inclusion's final state, or, in the more general case, the similar trajectory which is a minimizer of an max-(or Choquet) integral. The theorem is proved that formulates necessary conditions of optimality for the mentioned problem, conditions which in certain cases are also sufficient. [ABSTRACT FROM AUTHOR]

In this work, we studied the Borel masses relation used in QCD Sum Rules (QCDSR) calculations. These masses are the parameters of the Borel transform used when the three point function is calculated. We analised an usual and a more general linear relations. We concluded that a general linear relation between these masses provides the best results regarding the standard deviation. [ABSTRACT FROM AUTHOR]

In the following we present the most important properties of positive measures on Borel sets. [ABSTRACT FROM AUTHOR]