# Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 2012, vol. 12, iss. 4

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## Content

### Mathematics

Grebennikova I. V.
The problem of optimal control for singularly perturbed system with delay with integral quadratic con-straints
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3

Novikov E. A.
Algorithm of integrating stiff problems using the explicit and implicit methods
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19

Stepanenko D. S.
On verification of Brauer's theorem concerning Artin's L-functions of number fields
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31

Fadeev A. A.
Necessary and sufficient conditions of belonging to the Besov–Potapov classes and Fourier coefficients with respect to multiplicative systems
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41

Fedoseev A. E.
Inverse problem for Sturm–Liouville operator on the half-line having nonintegrable singularity in an interior point
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49

### Mechanics

Glukhova O. E., Glukhova O. E., Kossovich E. L., Fadeev A. A.
Mechanical properties study for graphene sheets of various size
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63

Glukhova O. E., Kirillova I. V., Slepchenkov M. M., Shunaev V. V.
Theoretical investigation of the deformed graphene nanostructures
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66

Kovalev V. A., Radaev Y. N.
On precisely conserved quantities of coupled micropolar thermoelastic field
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71

Manzhirov A. V., Kurdina S. P., Kuchumov A. G.
The conformal contact between punches and coated solids with complicated surface profile
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80

Manzhosov V. K., Novikova I. A.
The transformation of longitudinal the strain wafe having a linear form and increasing intensity in conjugation of rods with elastic gacket
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90

Tirimov A. A.
Graph approach for finite-element based model of an elastic body under conditions of axisymmetric deformation
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96

Schuchkina O. A., Golyadkina A. A., Aristambekova A. V., Potapov D. Y.
Numerical analysis of renal artery pathologies
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107