282 research outputs found
An elementary proof of the irrationality of Tschakaloff series
We present a new proof of the irrationality of values of the series
in both qualitative and
quantitative forms. The proof is based on a hypergeometric construction of
rational approximations to .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
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
Properties of odd nuclei and the impact of time-odd mean fields: A systematic Skyrme-Hartree-Fock analysis
We present a systematic analysis of the description of odd nuclei by the
Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and
blocking of the odd nucleon. Current and spin densities in the Skyrme
functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on
basic properties (binding energies, odd-even staggering, separation energies
and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6,
and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z <
92 are considered. The calculations demonstrate that the TOMF effect is
generally small, although not fully negligible. The influence of the Skyrme
parameterization and the consistency of the calculations are much more
important. With a proper choice of the parameterization, a good description of
binding energies and their differences is obtained, comparable to that for even
nuclei. The description of low-energy excitation spectra of odd nuclei is of
varying quality depending on the nucleus
A nonperturbative model for the strong running coupling within potential approach
A nonperturbative model for the QCD invariant charge, which contains no
low-energy unphysical singularities and possesses an elevated higher loop
corrections stability, is developed in the framework of potential approach. The
static quark-antiquark potential is constructed by making use of the proposed
model for the strong running coupling. The obtained result coincides with the
perturbative potential at small distances and agrees with relevant lattice
simulation data in the nonperturbative physically-relevant region. The
developed model yields a reasonable value of the QCD scale parameter, which is
consistent with its previous estimations obtained within potential approach.Comment: 14 pages, 4 figure
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