Андрей Ермоленко – Page 3 – Bulletin of Syktyvkar University

Bulletin 3 (36) 2020

by

I Kalinin S. I., Leonteva N. V. .(1/2; 1)-convex function. Part 2.

DOI: 10.34130/1992-2752_2020_3_04

Kalinin Sergey — Doctor of Education, Ph.D. in Physics and Mathematics, Professor, Department of Fundamental Mathematics, Vyatka State University, e-mail: kalinin_gu@mail.ru

Leonteva Natalia — Ph.D., Associate Professor of the Department of mathematics and computer science, Glazovsky state pedagogical Institute named after V. G. Korolenko, e-mail: leonteva-natalia-0812@yandex.ru

This article studies the (1/2; 1)-convex functions properties. Especially the paper describes that within the (1/2; 1)-convexity interspace this functions are continuous. Classical Hermite-Hadamard inequality analogue for the convex and concave functions on the segment are introduced. Besides
for discussed functions Jensen’s inequality and his analogue are proved.

Keywords: convex functions, concave functions, Hermite-Hadamard inequality, Jensen’s inequality.

References

Kalinin S. I., Leontieva N. V. (1/2; 1)-vypuklyve funktsii ( (1/2; 1) convex functions. Part I)), Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2018, > 1 (26), pp. 97-104.
Vinogradov O. L. Matematicheskiy analiz: uchebnik (Mathematical analysis: textbook), SPb.: BHV-Petersburg, 2017, 752 p.
Kalinin S. I., Pankratova L. V. Neravenstva Ermita – Adamara: obrazovatel’no-istoricheskiv aspekt (Hermite – Hadamard Inequalities: educational and historical aspect), Mathematical education, 2018, № 3 (87), pp. 17-31.
Abramovich S., KlariCic Bakula M., Matic M., PeCaric J. A variant of Jensen-Steffensen’s inequality and quasi-arithmetic means, J. Math. Anal. Applies., 307 (2005), pp. 370-385.

For citation: Kalinin S. I., Leonteva N. V. (1/2; 1)-convex function. Part 2., Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 3 (36), pp. 4-23.

II Komarov I. A., Makarov Р. A., Ustyugov V. A. On the free mechanical vibrations in a drv-friction system

DOI: 10.34130/1992-2752_2020_3_24

Komarov Ilja — Student, Pitirim Sorokin Syktyvkar State University, e-mail: mkrvpa@gmail.com

Makarov Pavel — Ph.D., Assistant Professor of Radio Physics and Electronics, Pitirim Sorokin Syktyvkar State University, e-mail: mkrvpa@gmail.com

Ustyugov Vladimir — Ph.D. in Physics and Mathematics, Department of Radiophysics and Electronics, Pitirim Sorokin Syktyvkar State University, e-mail: ustyugovva@gmail.com

The basic model of free oscillations with dry friction is developed. The classification of free oscillatory systems is performed. The inhomogeneous Lagrange equations of the second kind was solves in the case of a homogenous, static, low-velocity system. The conditions under which the
system is stationary, and also accomplish «stable» and aperiodic oscillations was determined.

Keywords: free oscillations, dry friction, Amonton—Coulomb’s law.

References

Jellett J. H. Traktat po teorii treniya (A treatise on the theory of friction), M. – Izhevsk: NIC «Regular and chaotic dynamics», 2009, 264 p.
Rosenblat G. M. Sukhoye treniye i odnostoronniye svyazi v mekhanike tvordogo tela (Dry friction and one-sided connections in solid mechanics), M.: URSS, 2010, 205 p.
Andronov V. V., Zhuravlev V. F. Sukhoye treniye v zakonakh mekhaniki (Dry friction in the laws of mechanics), M. -Izhevsk: NIC «Regular and chaotic dynamics», 2010, 184 p.
Zhuravlev V. F. К istorii zakona sukhogo treniya (To the history of the law of dry friction), Solid mechanics, 2013, > 4, pp. 13-19.
Kozlov V. V. Lagranzheva mekhanika i sukhoye treniye (Lagrangian mechanics and dry friction), Nonlinear dynamics, 2010, V. 6, > 4, pp. 855-868.
Zhuravlev V. F. Otklik na rabotu V. V. Kozlova «Lagranzheva mekhanika i sukhoye treniye» (Response to the V. V. Kozlov work «Lagrangian mechanics and dry friction»), Nonlinear dynamics, 2011, V. 7, № 1, pp. 147-149.
Alekseev A. E. Nelinevnyve zakonv sukhogo treniya v kontaktnvkh zadachakh linevnov teorii uprugosti (Nonlinear laws of dry friction in contact problems of the linear theory of elasticity), Appl. mechanics and tech, phys., 2002, V. 43, > 4, pp. 161-169.
Bronovets М. A. et al. Eksperimental’naya ustanovka diva izucheniva treniya i iznashivaniya s imitatsiyey faktorov otkrytogo kosmosa (Experimental simulator of outer-space conditions for the study of friction and wear), Friction and wear, 2009, V. 30, > 6, pp. 529-532.
Alexandrov V. M., Bronovets M. A., Soldatenkov I. A. Matematicheskoye modelirovanive iznashivaniya podshipnika skol’zheniva v uslovivakh otkrytogo kosmosa (Mathematical modeling of sliding bearing wear in open space), Friction and wear, 2008, V. 29,№ 3, pp. 238-245.
Bronovets M. A., Zhuravlev V. F. Ob avtokolebanivakh v sistemakh izmereniva sil treniya (On self-excited vibrations in friction force measurement systems), Solid mechanics, 2012, > 3, pp. 3-11.
Akulenko L. D. et al. Kvazioptimal’nove upravlenive povorotom
tverdogo tela vokrug nepodvizhnov osi s uchetom treniya (Quasioptimal control of the rotation of a rigid body around a fixed axis, taking into account friction), Izv. RAS. Theory and control systems, 2015, № 3, pp. 3-20.
Sviridenok A. I., Mechikov V. V. Trenive skol’zheniva polimernvkh kompozitov v uslovivakh vvsokikh skorostev (Sliding friction of polymer composites at high speeds), Friction and wear, 2005, V. 26, № 1, pp. 38-42.
Kolubaev A. V. et al. Generatsiya zvuka pri trenii skol’zheniva (Sound Generation During Slide Friction), JTF Lett., 2005, V. 31,
Chernousko F. L., Bolotnik N. N. Mobil’nyye robotv, upravlvayemyve dvizhenivem vnutrennikh tel (Mobile robots controlled by the motion of internal bodies), Tr. IMM URO RAS, 2010, V. 16, # 5, pp. 213-222.
Bolotnik N. N., Nunuparov A. M., Chashchukhin V. G. Kapsul’nvv vibratsionnvy robot s elektromagnitnvm privodom i vozvratnov pruzhinoy: dinamika i upravlenive dvizhenivem (Capsuletype vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion), Izv. RAS. Theory and control systems, 2016, .V”6. pp. 146-160. О свободных механических колебаниях 51
Deng Z. et al. Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale, Nature Mater, 2012, V. 11, pp. 1032-1037.
Panovko Y. G. Vvedeniye v teoriyu mekhanicheskikh kolebaniy (Introduction to the theory of mechanical oscillations), M.: Nauka, 1991, 256 p.
Magnus K. Kolebaniya: Vvedeniye v issledovaniye kolebatel’nykh sistem (Oscillations: An Introduction to the Study of Oscillating Systems), M.: Mir, 1982, 304 p.
Lojcjanskij L. G., Lurye A. I. Kurs teoreticheskoy mekhaniki. T. II. Dinamika (Theoretical Mechanics course. T. II. Dinamics), M.: Nauka, 1983, 640 p.
Makarov P. A. О variatsionnvkh printsipakh mekhaniki konservativnvkh i nekonservativnvkh sistem (On variational principles of mechanics applied to the motion of conservative and non-conservative systems), Vestnik of Syktyvkar State University. Ser. 1: Mathematics. Mechanics. Informatics, 2017, Rel. 2 (23), pp. 46-59.

For citation: Komarov I. A., Makarov P. A., Ustyugov V. A. On the free mechanical vibrations in a drv-friction system, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 3 (36), pp. 24-51.

III Suleimanova S.Sh. Dissipation of the energy of an alternating electric field in the half-space of an electron plasma with diffuse boundary conditions

DOI: 10.34130/1992-2752_2020_3_52

Suleymanova Sevda Shirin kyzy — Postgraduate Student, Bauman Moscow state Technical University (national research University), Moscow Polytechnic University, e-mail: sevda-s@yandex.ru

The magnitude of the absorption of the energy of the electromagnetic field in the half-space of the electron plasma is calculated. The case with an arbitrary degree of degeneracy of the electron gas is considered. To determine the absorption, a solution is used of the boundary-value problem
of the behavior (oscillations) of an electron plasma in a half-space with mirror boundary conditions for electrons. The Vlasov — Boltzmann kinetic equation with the collision integral of the BGK type (Bhatnagar, Gross, Kruk) and the Poisson equation for the electric field are applied. The
electron distribution function and the electric field inside the plasma are obtained in the form of expansions in eigen-solutions of the original system of equations. The coefficients of these expansions are found for the case of diffuse boundary conditions. The contribution of the surface to absorption is analyzed. Cases of various degrees of degeneracy of the electron gas are
considered. It is shown that the ratio of the frequency of changes in the electric field and the frequency of bulk electron collisions has a significant effect on the absorption of energy of the electric field near the surface.

Keywords: Vlasov-Boltzmann equation, collision frequency, electric field, Drude, Debye, van Campen modes, dispersion function.

References

Keller O. Local fields in the electrodynamics of mesoscopic media, Physics Reports, 1996, Vol. 268, pp. 85-262.
Girard C., Joachim C. and Gauthier S. The physics of the nearfield, Rep. Prog. Phys., 2000, Vol. 63, pp. 893—938.
Pitarke J. M., Silkin V. M., Chulkov E. V. and Echenique P. M. Theory of surface plasmons and surface-plasmon polaritons, Rep. Prog. Phys., 2007, Vol. 70, pp. 1—87.
Bozhevolnyi S. I. Plasmonics Nanoguides and Circuits, Singapore: Pan Stanford Publishing, 2008, 452 p.
Latyshev A. V., Suleimanova S. Sh. Analiticheskoye reshenive zadachi о kolebaniyakh plazmy v poluprostranstve s diffuznymi granichnvmi uslovivami (Analytical solution of the problem of plasma oscillations in a half-space with diffuse boundary conditions), Zh. vych. Matem. and math, physics, 2018, Vol. 58, No. 9, pp. 1562-1580.
Suleimanova S. Sh., Yushkanov A. A. Dissipatsiva energii peremennogo elektricheskogo polva v poluprostranstve elektronnov plazmy s zerkal’nvmi granichnvmi uslovivami (Dissipation of the energy of an alternating electric held in a half-space electron plasma with mirror boundary conditions), Plasma physics, 2018, Vol. 44, No. 10, pp. 820-831.
Lifshits E. M., Pitaevsky L. P. Fizicheskava kinetika (Physical kinetics), M.: Nauka, 1979. 527 p.

For citation: Suleimanova S.Sh. Dissipation of the energy of an alternating electric held in the half-space of an electron plasma with diffuse boundary conditions, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 3 (36), pp. 52-63.

IV Odyniec W. Р. About some mathematicians from the Polytechnic Institute in Leningrad perished in 1941-1943

DOI: 10.34130/1992-2752_2020_3_64

Odyniec Vladimir — Doctor of Physical and Mathematical Sciences, Professor, Pitirim Sorokin Syktyvkar State University, e-mail: W.P.Odyniec@mail.ru

The life and work of several mathematicians from the Polytechnic Institute in prewar Leningrad are described. All of them (N. A. Rosenson, T. N. Blinchikov, A. C. Nvrkova, M. S. Eleckv, V. I. Nikonov, M. A. Gelbcke, N. N. Gernet) perished in 1941-1943.

Keywords: N. A. Rosenson, T. N. Blinchikov, A. G. Nyrkova, M. S. Elecky, V. I. Nikonov, M. A. Gelbcke, N. N. Gernet, Riemanni spaces of the 1st class, Warinng problem, asymptotics of iterated functions, Szasz problem, fractional parts of a function of two variables, calculus of variations, Lagrange series.

References

Matematika v SSSR za sorok let. Biobibliografiya, T. 2 (The URSS Mathematics for forty years:1917-1957, Biobibliography, Vol. 2), M.: Fizmatlit, 1959, 819 p.
Sinkevich G. I. Nikolai Maksimovich Gunter (1871-1941) (Nicholas Maximovich Giinther (1871-1941)), Matematika v vysshem obrazovanii, 17 (2019), pp. 123-146.
Nauchnye rabotniki Leningrada (Members of staff of scientific for
Leningrad), L.: Izd-vo AN SSSR, 1934, 723 p.
Alersandrov A. D. Geometriva v Leningradskom universitete (The Geometry at Leningrad University), Vestnik Leningradskogo universiteta, № 11, 1947, pp. 124-148.
Odyniec W. P. О leningradskih matematikah, pogibshih v 1941-1944 godah (On some Leningrad based Mathematician perished in 1941-1944), Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2020, 122 p.
Dissertacii, zashtchishtchennye v Leningradskom ordena Lenina gosudarstvennom universitete im. A. A. Zhdanova v 1934~1954 gg (Bibliograficheskii ukazatel) ( Dissertations defended at the Leningrad State University named after A.A. Zhdanov decorated with to Order of long 1934-1954, (Bibliographical indicator), L.: Izdatelstvo Leningradskogo uni-ta, 1955.
Rosenson N. A. Differencialnye invarianty Rimanova prostranstva (Differential invariants of a Riemann spaces), L.: Trudy LIL, Razdel Fiz.-mat., T. 10, > 3, 1936, pp. 57-75.
Rosenson N. A. Differencialnye invarianty Rimanova prostranstva (Differential invariants of a Riemann spaces. Part II), L.: Trudy LIL, Razdel Fiz.-mat., T. 4, № 2, 1937, pp. 59-84.
Rosenson N. A. Nekotorye neravenstva iz teorii kvadratichnyh form (Some inequality from the theory quadratic forms), L.: Trudy LIL, Razdel Fiz.-mat., T. 4, № 2, 1937, pp. 85-93.
Trudy seminara ро vektornomu i tenzornomu analizu s ih prilozheniyami k geometrii, mehanike Ifizike, 6 (Proceedings of the seminar on vector and tensor analysis with its applications to geometry, mechanics and physics. 6), M.: OGIZ, Gos. izd-vo tehn.-teor,lit-rv, 1948, 515 p.
Rosenson N. A. О Rimanovvh prostranstvah klassa 1 (Upon Riemann Spaces of the Class 1), Izvestiya AN SSSR, Ser. matem, 4, 1940, pp. 181-192.
Rosenson N. A. О Rimanovvh prostranstvah klassa 1. Chast’ II (Upon Riemann Spaces of the Class 1. Part II), Izvestiya AN SSSR, Ser. matem. 5, 1941, pp. 325-351.
Rosenson N. A. О Rimanovvh prostranstvah klassa 1. Chast’ III (Upon Riemann Spaces of the Class 1. Part III), Izvestiya AN SSSR, Ser. matem, 7, 1943, pp. 253-284.
Kniga pamyati, Leningrad 1941-1945. Frunzenskiy rayon, T. 13 (The book of Memory, Leningrad 1941-1945, the Frunze district. Vol. 13), SPb.: Notabene, 1997. 515 p.
Kagan V. F. Nina Arkad’evna Rosenson (1909-1942) (nekrolog), (Nina Arkadyevna Rosenson (1909-1942) (Obituary), Izvestiya AN SSSR, Ser. Matem., T. 7., vvp. 6, 1943, pp. 251-252.
Blokada 1941-1944- Kniga pamyati, Leningrad, T. 25, P-R. (Prokof’evRessovskava) (Blockade 1941-1944. The book of Memory, Leningrad, Vol. 25), SPb.: Stella, 2005, 714 p.
Dvadcat’ let inzhenerno-fizicheskogo fakulteta LII (The twenty years of the department of engineering and physics of Leningrad Industrial Institute), L.: Izdatelstvo LII, 1939, 68 p.
Kniga pamyati (The book of Memory), Sostaviteli: S. A. Sirotkina, E. F. Tarasov, SPb.: Izd-vo SPbGTU, 2000, 90 p.
Nyrkova A. G. О polozhitelhyh trigonometricheskih summah (On positive trigonometrical sums), L.: Trudy LIL, Razdel Fiz.-mat. 3:1,1939, pp. 5-10.
Nyrkova A. G. Zadacha Szasz’a (Szasz Problem), L.: Trudy Politehnicheskogo instituta, 3, 1941, pp. 50-59.
Nikonov V. I. Asimptoticheskie vyrazheniya iterirovannyh funkcyi (Asymptotic expressions to Iterated functions), L.: Trudy LIL Razdel Fiz.-mat, 5:1, 1938, pp. 33-56.
Nikonov V. I. Integralnye predstavlenie nekotoryh trigonometricheskih polinomov kak sposob ih izucheniya (The integral representation of some trigonometric polynomials is a method of their study), L.: Trudy LII., Razdel Fiz.-mat., 3:1, 1939, pp. 11-15.
Blokada 1941-1944- Kniga pamyati, Leningrad, T. 22, N-P (NikolaevaPavlova) (Blockade 1941-1944. The book of Memory, Leningrad, Vol. 22), SPb.: Stella, 2005, 716 p.
Gelbcke M. A. Ob asimptoticheskom vyrazhenii summv drobnvh chastei funkcii dvuh peremennvh (On an asymptotic expression of the sum of fractional parts of a two-variable function), Zhurnal Leninqradskoqo Fiziko-matematicheskoqo obshtchestva, T. 1, Vyp. 2,
1927, pp. 281-298.
Gelbcke M. A. Otnositelno g(k) v problemie Varinga (Relating g(k) to Waring problem), Izvestiya AN SSSR, VII seriva, Otd. matematicheskih I estestvennvh nauk, 1933, vyp. 5, pp. 631-640.
Trudy 2-go Vsesouznogo s’ezda matematikov (Leningrad, 24-30 iunya 1934), T. 1 Plenarnye i obzornye doklady (Proceedings of the 2nd All Union Congress of Mathematicians. Leningrad, June 24-30, 1934, Vol.l , Plenary and survey reports), L.-M.: Izd-vo AN SSSR, 1935, 469 p.
Vachromeeva О. B. Professor matematiki Nadezhda Nikolaevna Gernet (1877-1943), (Professor of Mathematics Nadezhda Nikolaevna Gernet (1877-1943)), Vestnik Nizhegorodskogo gosudarstvennogo universiteta, № 4 (116), 2019, pp. 105-109.

For citation: Odvniec W. P. About some mathematicians from the Polytechnic Institute in Leningrad perished in 1941-1943, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 3 (36), pp. 64-86.

V Yermolenko А. V., Ladanova S. V. Contact problem for two plates with different fixing

DOI: 10.34130/1992-2752_2020_3_87

Yermolenko Andrey — Ph.D. in Physics and Mathematics, Associate Professor, Head ofthe Department of Applied Mathematics and Information Technologies in Education, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

Ladanova Svetlana — Student, Pitirim Sorokin Syktyvkar State University, e-mail: ea74@list.ru

An analytical solution for two plates is given using the classical theory of bending of flat plates. In this case, one plate is hinged, the second has a rigid fastening. It is shown that when using the Sophie Germain-Lagrange equation, contact reactions contain concentrated forces.

Keywords: plate, contact problem, Sophie Germain-Lagrange equation, analytical solution.

References

Mikhailovskii E. I. Shkola mekhaniki obolochek akademika Novozhilova (School of Shell Mechanics Academician Novozhilov), Syktyvkar: Izd-vo Svkt. un-ta, 2005, 172 p.92 Ермоленко А. В., Ладанова С. В.
Mikhailovskii Е. I., Tarasov V. N. О sxodimosti metoda obobshhennoj reakcii v kontaktny’x zadachax so svobodnoj granicej (On the convergence of the generalized reaction method in contact problems with a free boundary), Journal ofApplied Mathematics and Mechanics, 1993, v. 57, № 1, pp. 128-136.
Yermolenko A. V., Mikhailovskii E. I. Granichnye uslovija dlja podkreplennogo kraja v teorii izgiba ploskih plastin Karmana (Boundary conditions for the reinforced edge in the Karman theory of bending of flat plates), MTT. 1998, > 3, pp. 73-85.
Mikhailovskii E. I., Badokin К. V., Yermolenko A. V. Teorija izgiba plastin tipa Karmana bez gipotez Kirhgofa (The theory of bending of Karman-tvpe plates without the Kirchhoff’s hypotheses), Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics, 1999, 3, pp. 181-202.
Mikhailovskii E. I., Yermolenko A. V., Mironov V. V., Tulubenskaya Ye. V. Utochnennyye nelineynyye uravneniya v neklassicheskikh zadachakh mekhaniki obolochek : Uchebnoye posobiye (Refined nonlinear equations in nonclassical problems of shell mechanics: Textbook), Syktyvkar: Izd-vo Syktvvkarskogo un-ta, 2009, 141 p.
Mikhailovskii E. I., Toropov A. V. Matematicheskiye modeli teorii uprugosti (Mathematical models of the theory of elasticity), Syktyvkar: Svkt Publishing House. University, 1995, 251 p.
Grigolyuk E. I., Tolkachev V. M. Kontaktnyye zadachi teorii plastin i obolochek (Contact problems in the theory of plates and shells), M.: Mashinostroyeniye, 1980, 411 p.

For citation: Yermolenko А. V., Ladanova S. V. Contact problem for two plates with different fixing, Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Informatics, 2020, 3 (36), pp. 87-92.

Bulletin 6 2006

by

I. Antonova N.A. Dynamics in pulse-frequency-modulated control systems

Conditions are obtained for existence of mT-periodic modes (m = 1, 2, 3) in one dimensional control systems employing pulse-frequency modulation of the first and second kinds.

II. Bazhenov I.I. The property of nonatomicity for set families and vector measures

We introduce the new concept of atom for family of subsets of some set. This notion coincides with the notion of atom of vector measure if the family in question contains only sets of zero measure. Sufficient conditions of nonatomicity of family of sets are given for one special case. We also establish sufficient conditions of nonatomicity of the vector measure n(E) = φ(m(E)) constructed by means of linear and continuous operator φ and vector measure m with values in topological vector space.

III. Veksler A.I., Koldunov A.V. On the normed lattice and its normed completion

Here (negative) answers on two problems conserning the relations between properties of a normed lattice and its normed completion are presented.

IV. Vorobyova E.V. Some ergodic properties of the homogeneous Markov chain with the continuous parameter

We prove for any Markov chain with finite space of states that the final probabilities vector is orthogonal to the columns of generator. And in the case of any discrete space of states we find an explicit formula for final probabilities in terms of the generator’s resolvent.

V. Zvonilov V.I. Rigid Isotopies of Trinomial Curves with the Maximal Number of Ovals

Let l be the number of ovals of nonsingular real trinomial curve уⁿ + b(x)у + w(x) = 0. In this paper the sharp upper bound for l is found for any n. The rigid isotopy is understood as a path in the space of nonsingular real trinomial curves with n fixed. The rigid isotopy classification of such curves with the maximal l is given. In particular case n=3 the rigid isotopy classification of trigonal M-curves is obtained.

VI. Golovach P.A. Distance constrained labelings of trees

An assignment of nonnegative integers to the vertices of a graph G is L(p₁, p₂, … , p_k) – labeling (or coloring) if for every two vertices at distance at most i <= k, the difference of the integers (labels) assigned to them is at least p_i. An interest to such labelings is motivated by their usage in models of telecommunication networks. We prove that the existence problem of L(p, 1, 1) – labeling with labels, that are at most λ, is NP-complete for trees.

VII. Yermolenko A.V. The calculation of round plates with refined theories

The Karman-Timoshenko-Naghdi type equations are used for the calculation of round plates with rigid boundary. The problem is solved not using additional condition about transversal shears on boudary.

VIII. Zheludev V.A., Pevnyi А.В. Discrete periodic frames

We construct the filter bank of perfect reconstruction for the discrete N-periodic signals. This bank generates the wavelet tight frames in the spaces C^N and R^N.

IX. Malozemov V.N., Pevnyi А.В., Selyaninova N.A. Primal lifting scheme

We present the analysis of the primal lifting scheme for the constructing of the wavelet decomposition of the discrete periodic signals. A description of the set of all control functions β_ν(k) is given.

X. Mironov V.V. The account of transversal shears in a problem about a bend of the cylindrical panel

In this paper the task about a bend of cylindrical panel under effect of normal load is considiered. The normal load are distributed on field, simular to middle surface of a panel. The bend of panel on register of transversal shears by S.P. Timoshenko’s model is described. The mechanism of dependence of a momemts for transversal shears is confirmed — the graphics of moments for change of curvature of middle surface and for change of transversal shears are be in anti-phases in fields of a maximal absolute values.

XI. Mikhailovskii E.I. The classical linear theory of shells

The equations and the boundary values of the modern classical linear theory are consecutively obtained. On equations’ deduction the Novozhilov-Finkel’shtein criterion was used to estimate the Kirchhoff-Love hypotheses. The final variant of shells’ theory includes the deformation boundary values, which were obtained by K.F. Chernykh for one-related middle surface and were generalized by the author of article for multirelated middle surface. It is shown that the compatibility conditions can be obtained directly from the equilibrium equations of shells’ theory; initially condition was obtained by A.L. Gol’denweiser from the Gauss-Petersson-Kodacci equations for deformed middle surface. The author’s operation form is used for recording the general equations of the linear shells’ theory.

XII. Nikitenkov V.L. On the integer-valued solving of the linear cutting problem

It was proved that optimal value of the target function for the integer-valued problem of linear cutting just slightly differs from the corresponding value for the linear cutting problem. On this basis it was offered the effective complex algorithm of integer-valued problem solution.

XIII. Ezovskih V.E. Color sampling algorithms

Three algorithms of color sampling suitable for color conversion are considered. Some practical features of realization are briefly discussed.

XIV. Kotyrlo E.S. Methods of labor market demand prediction in professional skills structure

The problem of labor demand prediction in professional skills structure is one of the main problems that impact on the labor market equilibrium and human capital efficiency. In this article prediction methods and their efficiency to using in labor market are analyzed; an analytic model of labor demand prediction in professional skills structure is constructed; a version of statistical survey execution is suggested.

XV. Mironov V.V., Kuznetsova N.V. The task about axis-symmetrical eigen-oscillations of round rigidly fixed plates

In this paper the task about axis-symmetrical eigen-oscillation of round rigidly fixed plates is considiered. The analytical solution is given.

XVI. Nikitenkov V.L., Sakovnich D.J. Realization of complex algorithm for integer-valued problem of linear cutting

Complex method for solving of integer-valued problem of linear cutting are considered. The results of testing on enterprize are describe.

XVII. Nikitenkov V.L., Yasinsky V.I. Web-services of complex algorithm for integer-valued problem of linear cutting

The problems of working over a network and the Internet, the superiority of Web-services over the other server-applications, a short description of the applied Web-service and the examples of Web-service query are discussed.

XVIII. Pevnyi А.В., Istomina M.N. Mercedes-Benz frame in n-dimensional space

We construct an equal-norm tight frame in Rn consisting of n+1 vectors. The angles between any different vectors are equal π/2 + arcsin(1/n).

XIX. Poroshkin A.G., Gabova M.N., Grelya E.N. On the Arzela – Borel theorem.

Let X be a topological space, (Y, V) — uniform space and (f_α) be a sequence or directedness of functions f_α : X —> Y. In this paper autors prove the generalization of Arzela — Borel theorem: when f_α ϵ C(X) ∀α and f_α(x) —> f(x) ∀x ϵ X, then f ϵ C(X) if and only if f_α converges to f on X quasi-uniformly.

XX. Tarasov V.N., Pavlova L.A. The proof of geometric theorems by means of computer algebra

Some geometric theorems can be stated in coordinate form as polynomials in algebra and can be proved by algorithmic methods. In article the theorems of Pascal and Pappe Alexandrinian are prooved by means of computer algebra. Also some properties of Torricellian point for arbitrary tetrahedron are stated.

Bulletin 7 2007

by

I. Vechtomov E.M., Starostina O.V. Generalized Abelian-regular positive semirings

Text

Notions of generalized Abelian-regular positive semirings (arp-semirings) and generalized Boolean semirings are introduced. It is showed that the research of generalized arp-semirings reduces to arp-semirings. Functional representation of generalized arp-semirings and generalized Boolean semirings are obtained. Dauns-Hofmann’s theorem about representation of biregular rings is extended on biregular semirings.

II. Lovyagin Yuri N. Hyperrational numbers as the basis of analysis

Theory of hyperrational numbers as the basis of analysis is considered. The main aspects of the theory are adduced. Analogs of the classical differential and integral calculus of one-variable function theorems are stated.

III. Odyniec W.P., Prophet M.P. On three forgotten results of S.Krein, N.Bogolyubov and V.Gurari with applications to bernstein operators

The results of M. Frechet in 1934 about the largesteigenvalue of a stochastic matrix [6] attracted attentionto positive linear operators with norm 1. The study of compact linearoperators with stochastic kernel by N.M. Krylov and N.N.Bogolyubov during the 1930’s ([9], [10]) was generalized by S. Krein and N.N. Bogolyubov a decade later in [2]. These results contributed to the 1968 paper [8] of M. Krasnoselski in which the problem of determining minimal-normshape-preserving projections was present. Unfortunately, many of these papers are practically unknown, as they were published in the Ukrainian language. On the other hand, recent developments in the theory of minimal shape-preserving projections have been made using methodsthat are independent of Krasnoselski’s work (see [3] and [11]). In this paper, we attempt to connect these two directions by studying the (so called) Bernstein operators.

IV. Prazdnikova El. Wl. Modelling the real analysis in the framework of axiomatic of hypernatural numbers

In the paper formalized theory of Non-Standard theory of numbers and formalized theory of hyperrational numbers are stated. The main theorems of classical differential calculus are modelled.

V. Savelev L.J., Ogorodnikov V.A., Sereseva O.V. Stochastic model of piecewise linear process

The stochastic process with piecewise linear trajectories is considered. The process is based on models of stochastic walk on a straight line. The distributions of stochastic variables, forming this process, and, in particular, distribution of relative time expectations for Poisson flow of points are investigated. The appropriate mathematical expressions for these distributions, and also expressions for mean of process as time-varying function are received.

VI. Mikhailovskii E.I. A non-linear theory of flexible shells Zhuravsky-type

A non-linear theory of flexible shells has been built, taking into account transversal shears by D. I. Zhuravsky model, By introducing generalized forces and moments the equations are reduced to the kind formally coinciding whith equations in the theory of shells, based on Kirchhoff’s hypotheses. This allows to formulate an effective algorithm of accounting transversal deformations in some of Kirchhoff’s variations of the theory of shells and planes, The algorithm is illustrated by more exact specification of K. Margyerre’s non-linear theory of shallow shells.

VII. Duriagin A.M. Real harmonic frames, toughness and redundancy

It was proved that real harmonic frames possess maximal redundancy, i.e. if any m-n vectors are deleted then remaining n vectors form frame in Rⁿ (in the general case, it is not tight frame). The fast frame expansion algorithm is offered.

VIII. Kholmogorov D.V., Tarasov V.N. Influence of boundary conditions on the stability of a cylindrical shell

In the work the problem of stability of the cylindrical shell, loaded with external normal pressure or undergoing axial compression, is examined. With a numerical study the tasks of displacement are approximated by splines. In contrast to the traditional trigonometric series the application of splines makes it possible to consider the real boundary condition, in particular, the displacement of the ends of shell as rigid whole is allowed.

IX. Mikhailovskii E.I., Mironov V.V., Kuznetsova J.L. About one solution algorithm for solving of nonlinear boundary problem Karman-type

On the basis of Green’s well-known function, an algorithm of edge problems with Karman-type non-linearity to the corresponding system of algebraic equations. The algorithm is realized on tne examples of simply supported opened cylindrical shell.

X. Pevnyi А.В., Istomina M.N. Recovery of the signal in the case when one frame coefficient is erased

The authors consider Mercedes-Benz frame and frame expansions for every vector x ϵ Rⁿ. In the case when one frame coefficient is erased the authors suggest a fast algorithm for the recovery of the vector x.

XI. Malozemov V.N., Pevnyi A.B. Mercedes-Benz systems and tight frames

The paper is for the section “Easy Reading for Professionals”. The authors study the tight frames in the space in Rⁿ. A complete description of the tight frames in Rⁿ consisting of n+1 vectors is given. An exact lover bound for the frame potential is proved.

Bulletin 8 2008

by

I. Balakin S.V. Runs characteristics in a ternary Marcov Chain

A ternary Markov chain is considered. There are functionals concerned with a number of events and a number of runs. Probability generating functions for joint distributions of this functionals are obtained. Precise formulas for expectations, variances and covariations are founded.

II. Vechtomov E.M., Chuprakov D.V. Congruences on semirings of continious functions and F-spaces

The congruences of semirings of non-negative continuous functions on topological space are investigated. In terms such congruences new algebraic characterizations of F-spaces and P-spaces are received.

III. Mekler A.A. On positive integer characteriyation of regular variyng quasi-concave modulars

The initiated in [1] study of the correspondence between quasi-concave modulars and sequences of positive integers is continued. In the presented paper are examenated especially regularly variying quasi-concave modulars. It is stated in Theorems 9, that a sequence of positive integers corresponds to a fast variyng quasi-concave modular (that means the case of regularity index α=0) iff it is equivalent to a integer sequence which tends to +∞. In Theorem 8 is proved that the sequence of positive integers corresponds to a slow variyng modular (the case of regularity index α=1) iff it is equivalent to a sequence of the form 211•••1211•••121••• •••••• where the lengths of blocks of units tends to +∞. In Theorem 5 the case of intermediate value of regularity index α: 0<α<1 is investigated.

IV. Savelev L.J. Extension of a measure up to integral

In this paper the task about a bend of cylindrical panel under effect of normal load is considiered. The normal load are distributed on field, simular to middle surface of a panel. The bend of panel on register of transversal shears by S.P.Timoshenko’s model is described. The mechanism of dependence of a moments for transversal shears is confirmed – the graphics of moments for change of curvature of middle surface and for change of transversal shears are be in anti-phases in fields of a maximal absolute values.

V. Belyaeva N.A. The structural models of deformation processes

Mathematical models of flow and deformation processes of materials with evolutionarizating structure are presented. The problems spread to wide sphere of structure-sensitive objects – from powder systems to polymer materials and composites. This models allow to define change of deformation, temperature and structure characteristics of varried systems in the various processing-hardening, non-Newtonian flow, solid-state extrusion.

VI. Nikitenkov V.L. Basic property of the optimal integer-valued solving of the linear cutting problem

It was proved that basic solution of the some modification linear cutting problem is optimal integer-valued solving of the integer cutting problem.

VII. Sakovnich D.Y. Singularity in the format cutting problem

In scope of format cutting problem the problem of minimization winder adjustments is considered. It was offered the method for getting the most singular solution if the problem.

VIII. Kluchnikov E.A. SOA data store and search system

The author consider SOA data store and search system written in Java. SOA approach makes such systems scalable and easy to integrate as basis of enterprise infrastructure. Java technology makes it easier to use the full power of modern servers.

IX. Simakov A.V. Parallel compression of huge images

In this paper we describe an efficient algorithm for parallel compression of huge images. The algorithm is based on wavelet transform. The article is focused on practical implementation and evaluation of this compression method. As a result, all described features are implemented in software library written in C language. This library and compression program is freely available through the Internet and distributed with full source code under the terms of Open Source GNU GPL license.

X. Poroshkin A.G., Popova L.A. Remark about the outer measures geneated by measures

It is proved that outer measures generated by measures in sense of Halmos, Vuklikh, Poroshkin are lower continuous, however the outer measure of Lebesque in R is not continuous from above and not exhaustive.

XI. Tarasov V.N., Andryukova V.Yu. On stability and supercritical behavior of a spherical shell

The problem of the spherical shell experiencing external normal pressure is considered. A precise formula is used for the calculation of the work of external forces. In the work a variational approach is applied. Cubic splines are used for the finite-dimensional approximation of displacements. The influence of nonlinear terms on the amount of the critical force is investigated.

XII. Tulubenskaya E.V., Kargin R.V. The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences

The stability of the longitudinally compressed shank with unconstant rigidity at the border of two Winkler’s ambiences is investigated. The algorithm is based on the local search variants.

XIII. Jakovlev V.D. On one way of introducing integrals in the high school mathematics

Bulletin 9 2009

by

I. Vechtomov E.M., Chuprakov D.V. Pseudo-complements in a lattice of congruence of semirings of continuous functions

We investigate the properties of lattice of congruencies of semirings and semifields of continuous nonnegative (positive) functions, set on an arbitrary topological space X. It’s proved that these lattices are lattices with pseudocomplements and every its element has not more than one complement. In terms of lattices of congruencies of semirings of continuous functions over X, the characterizations of some properties of space X are obtained.

II. Eltsov N.P., Ogorodnikov V.A., Prigarin S.M. Analysis of cascade models of random fields

The stochastic process with piecewise linear trajectories is considered. The process is based on models of stochastic walk on a sraight line. The distributions of stochastic variables forming this process, and, in particular, distribution of relative time expectations for Poisson flow of points are investigated. The appropriate mathematical expressions for these distributions, and also expressions for mean of process as time-varying function are received.

III. Lovyagin Yu.N., Prazdnikova E.Wl. Elementar functions on the set of complex hyperrational numbers

The basic elementary functions are enterd within the limits of the model-theoretic approach to the concept of complex hyperrational numbers. Their basic properties are resulted.

IV. Odyniec W.P. One differential inequality and its application to the Pearson’s distribution densities

We prove that for some large set of functions including the densities of Pearson distributions the condition 0<(f/f')'<1 is sufficient for differential inequality f''(t)*f(t)<(f'(t))² (Theorem 1). The application of Theorem 1 to the densities of Reason distributions is given.

V. Belyaeva N.A. Influence of the typical timeses on modes hardphase extrusion

There are difined qualitative different extrusion regimes – stationary, quasistationary, transient modes – on base of the comparison of the typical times of the structuring, compactions and extrusion processes.

VI. Bayborodina O.V., Sakovnich D.Y. Application of the complex algorithm for solving of size cutting problem in order to increase the efficiency of business processes of core production

The possibility to increase the efficiency of business processes of spiral winding cores production by implementing the complex algorithm for solving of integer- valued problem of linear cutting is investigated. The results of the comparison analysis of MSY used calculation and the complex algorithm on the actual data of MSY are given.

VII. Mikhailovskii E.I., Tulubenskaya E.V. The account of the transverse strain in the problem about stability of the cylindrical cover in the conditions constructive nonlinearity

In work is considered the problem about stability of longitudinal compressed simply supported the cylindrical cover located at the border of two Winkler’s ambiences. The specified theory of Margera-Timoshenko type is used. The problem is solved by the means of the combined algorithm variant search.

VIII. Tarasov V.N. Modeling the cell membrane potential of the sinoatrial node

The work of the heart associated with a regular contractions of muscle forming the heart wall. The heart rate caused by the spread of the electrical action potential (AP) on heart fibers. Most of these fibers can self-excite. This is in contrast to AP in the nerve cells. For self-excitation AP in neuronal cells requires a signal (current initialization). Sector of the heart, giving the excitation maximum value – it is sinoatrial node. In this paper a mathematical model of electrical activity of cells of the sinotrial node is proposed.

IX. Belyaeva N.A., Osipova V.V. The structural compaction model of viscoelastic composite material

The structural model of solidphase plunger compaction of porous viscoelastic material is presented. Decisions of problems for case of the set speed and pressure on plunger are received. The program complex in the programming environment Delphi is developed. Results of numerical experiment are presented.

X. Mikhailovskii E.I., Gintner V.V., Mironov V.V. Auxiliary operator method for solving linear boundary-value problem

Linear boundary-value problem with homogeneous boundary condition under certain Green function may be considered as solved. But analytical construction of Green function is very problematical even for a homogeneous linear boundary-value problem with variable coefficients. At the same time one can select (auxiliary) differential operator with the same order, as operator of considered problem, the one for which Green function of the original problem with the boundary condition is fairly simply computed. This article shows that in these cases the original boundary-value problem is reduced to a Fredholm integral equation of the first or second kind. For its solution, for example, method of mechanical quadrature can be used.

XI. Pevnyi A.B., Duriagin A.M. Spherical designs

Definition of spherical t-design is made. The example of 4-design R³ is presented. The designs on a plane is in detail investigated, it is possible to name them designs.

XII. Pevnyi A.B., Istomina M.N., Maksimenko V.V. Complementary tight frames

For any tight frame in the space Rⁿ consisting of m vectors, m>n, the authors construct a complimentary tight frame in the space of dimension n’=m-n.

XIII. Vechtomov E.M. About problems of high professional education in Russia

We are analyzing the state of affairs and exploring the contradictions in our high professional education. Our high education needs a modernization, but it should rely on reality in Russia and the traditions of fundamental education, not following western examples. Real education, moral upbringing and true science should be priorities of our government and society.

Bulletin 10 2009

by

I. Vechtomov E.M. Structure of semifields

This work is an analytic scientific review over the theory of semifields, sponsored by grant RFBR № 08-01-11000-ано.

II. Efimov D.B., Kostyakov I.V., Kuratov V.V. On exact representations for the group motions of Galilean plane
Text

The Pimenov algebra with two generators D₂ is defined and some of its properties are shown. Some exact two- and three-dimensional matrix D₂-representations for the group motions of Galilean plane (the Galilean group) are considered. A geometric interpretation of them is giving. We consider also a exact representation of the Galilean group by elements of Grassmann algebra.

III. Kostyakov I.V., Kuratov V.V. Massive Yang-Mills fields, translation and nonsemisimple gauge symmetry

Gauge fields of semisimple groups of internal symmetries are massless and require special techniques for their mass. Massive mechanisms usually contain translational transformations specific to nonsemisimple groups. We show that under the localization nonsemisimple internal symmetry gauge fields corresponding to generators of translation, are massive. In addition, we introduce nonlinear generalizations of well-known models, with local translational symmetry and as a result, the massive gauge fields. Thus, the local Galilean symmetry is realized on a special pair of scalar fields, leading to massive electrodynamics, and the localization of the Euclidean group leads to massive non-Abelian theory without matter fields. We propose a simple interpretation of the Stueckelberg mechanism.

IV. Tikhomirov A.N. On the circular law of random matrices

In review the new results on proving the circular law for random matrices are given. Among them are the results obtained by the author together with F.Gotze for rared non-Hermitian matrices of large dimension.

V. Malozemov V.N., Solov’eva N.A. On the frame matrix

The authors consider the following problem. Given positive-definite Hermitian matrix S and positive numbers a₁, … , a_m, m ≥ n, find a frame {φ₁, … , φ_m} in Cⁿ such that S is frame matrix and equations IIφ₁II = a₁, … , IIφ_mII = a_m hold. The authors give new proof of the theorem on necessary and sufficient conditions for existence of such frame.

VI. Podorov A.E., Sakovnich D.Y. Platform for testing methods of solving linear cutting problem

Common ideas of building applications for solving cutting problems were developed. Using these ideas, platform for testing algorithms was built. This platform was applied for compare some algorithms.

VII. Belyaeva N.A., Nikonova N.N. Structural model of extrusion with usage of the generalised model of Newton

The mathematical model of Solid-Phase is presented extrusion of a porous viscoelastic material with a condition of constancy of speed plunger the press. The results confirming rightfulness of replacement of the equation of movement on the equation of equilibrium are received. For the description of considered stream Lagrangian (mass) coordinates are used.

VIII. Belyaeva N.A., Spiridonov A.V. The structural models of deformation processes

The mathematical model of tverdofaznoy extrusion of porous viscoelastic material is presented with the condition of constancy of speed of plunzhera the press. Got results, confirm legitimacy of replacement of equalization of motion on equalization of equilibrium in the works before executed on this subject. For a chosen type of flow specification lagranzh(mass) coordinates are used.

IX. Vasilyev А.А., Koroleva А.N. Some applications of computational geometry to linear programming problems

The work considers one of the approaches to the solution of linear-programming problem with two variables: the one of computational geometry and its generalization on the problem of the least covering circle. Numerical approbation of the given method is carried out, the algorithm of the decision is constructed.

X. Nikitenkov V.L., Podorov A.E. Modifications of waste cutting problem

The problem of cutting materials with various length and limited stores is considered as the waste cutting problem. Five it’s modifications are offered. In some of them methods of a finding admissible inverse matrix are given. Results of numerical experiments are discussed.

XI. Yakovlev V.D., Afonin R.E. The hunting on numbers

In this article the history of search of amicable pairs since times of ancient Greeks and up to now is shown. Also current outcomes of search of aliquot sequences and Mersenne numbers are given.

Bulletin 11 2010

by

I. Mikhailovskii E.I. Word about Valentin Valentinovich Novozhilov

II. Mikhailovskii E.I., Tarasov V.N. The constructive – nonlinear mechanics of plates and shells

The review of the basic results obtained by authors and their disciples for last 20 years in the field of constructive-nonlinear mechanics of plates and shells is given. The general course of the proof proposed by authors of a method of the generalized reaction for the solving of contact problems with free boundary and a method of local search of eigenvalues of positively homogeneous operators for the solving of essentially nonlinear spectral problems is explained. Algorithms of local search of variants in a combination to their full search on a rare grid and with movement on parameter of rigidity of one of elastic environments are illustrated. Effect of accounting transversal deformations in the equations of mechanics of plates and shells is investigated.

III. Belyaeva N.A. Deformation of viscoelastic materials with changing structure

Deformation processes of materials with changeable structure is presentated. Worked out mathematical models are including wide field of objects beginning with systems-powder to polymer and composite materials. This models give a chance to define deformation, temperature and structure characteristicses during hardening, solid state extrusion and non-Newtonian flow.

IV. Tarasov V.N., Andryukova V.Yu. Of nonlinear fluctuations of rectangular plates

Linear and nonlinear fluctuations of rectangular plates are researched. The difference scheme for solving the dynamic equations of Karman is considered. The results of numerical experiments are analyzed, solutions obtained on the basis of a linear equations of vibrations of plates and the solutions obtained by numerical analysis of nonlinear Karman equations are compared.

V. Belyaev Y.N. Characteristic matrix of laered-periodic structure

The method of recurrent calculation of the matrix characterising distribution of elastic waves in periodic layered structure is offered. The estimation of efficiency of this method is made.

VI. Sergey G. Bobkov. The growth of L^{^p}-norms in presence of logarithmic sobolev inequalities

The growth of L^p-norms is considered under various hypotheses, including LS_q (logarithmic Sobolev) inequalities.

VII. Vechtomov E.M., Sidorov V.V. On difinability of semirings of continuous functions by their subalgebra lattice

It is solved the problem of semirings of continuous functions difinability by their subalgebra lattice. Namely, it is proved that an isomorphism of lattices of all subalgebras of semirings of continuous nonnegative functions over arbitrary topological spaces implies an isomorphism of semirings of continuous functions.

VIII. Petr A. Golovach, Pinar Heggernes. Choosability of P_₅-free graphs

A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k > 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we prove that the problem is fixed parameter tractable on P₅-free graphs when parameterized by k. This graph class contains the well known and widely studied class of cographs. Our result is surprising since the parameterized complexity of k-coloring is still open on P₅-free graphs. To give a complete picture, we show that the problem remains NP-hard on P₅-free graphs when k is a part of the input.

IX. Kostyakov I.V., Kuratov V.V. Limit transitions in gauge theories

We show how to obtain Lagrangians with nonsemisimple gauge symmetry, using contractions. The limit transitions of SO(2) and SU(2) gauge theories are considered

Bulletin 12 2010

by

I. Mikhailovskii E.I. Word about Valentin Valentinovich Novozhilov

II. Mikhailovskii E.I., Tarasov V.N. The constructive – nonlinear mechanics of plates and shells

Presents the second part of the article (the first part was published in the previous issue this “Messenger”: 2010.- Vyp.11 – C.5-51) devoted to the stability and supercritical behavior of stractures and structures in unilateral restractions on the movement. The article, as stated in the preface, is a review. However, as set out in this part of the method of motion in the parameter stiffness of the elastic medium is published for the first time.

III. Gryshchenko A.E., Kononov A.I., Mikhailova N.A. Study the scale effect by the birefringence method

Studied by the birefrigency method are the properties of surface layers of some polymers of various molecular composition. It was shown that surface layers are characterized with orientational order of chain-like molecules in the films.the thicknesses of optically anisotropic surface layers are shown to be in the range of 10-400 micrometers. It was concluded that the odserved “scale” effect should be taken into account in the studies of thin films properties. Such the effect results from the fact that the surface layers properties differ significantly from those ones in bulk volume.

IV. Yermolenko A.V. On the solution of inverse problems using the Кarman-Timoshenko-Naghdi type theory

The aim of this paper is to prove the role of the Karman-Timoshenko-Naghdi type theory on the solution of inverse problems. Inverse problems are considered for cylindrical plates and round axis-symmetric paltes.

V. Nikitenkov V.L., Kholopov A.A. The optimal parameters of an additive-split method (ASM)

An equation x = b – Ax in a Banach space with continuous linear operator A is solving by so cold additive-split method when operator is split to some parts and an appropriate iteration procedure is used. The optimal parameters of splitting are those to extend mostly the spectral region of convergence for a self-conjugate operator.

VI. Kluchnikov E.A. Web-application performance tuning

The problems of performance of Web applications and solutions. Result of the research is to create a productive template library based on dynamic code generation.

VII. Belyaeva N.A., Dovzhko E.S. Spherical product hardening with pressure in front of

The stress state of a formed spherical product is considered from the view of the body continuously increases. The full stress tensor is given on the growing surface. The pressure from the liquid layer on the formed solid part is taken into account.

VIII. Belyaeva N.A., Pryanishnikova E.A. Granularity in a nonisothermal extrusion composite material

The structural mathematical model of non-isothermal extrusion of a composite material using a generalized model of Newton is presented. The novelty of the proposed model is the joint consideration of Reo-Dimamics, kinetics of structuring and temperature factor.

IX. Mikhailovskii E.I., Holmogorov V.V., Gintner V.V. The longitudinal stability of a cylindrical shell at external and internal Winkler’s restrictions

In this paper the problem of stability of a cylindrical shell, subjected to longitudinal compression, in the conditions of external and internal one–sided constraint restrictions Winkler’s type is considered. The local method of search of eigenvalues of positively homogeneous operator is applied. In the numerical study of the problem displacements are approximated by splines.

X. Nikitenkov V.L., Tyufyakov A.V. Tetris-eliminator and the algorithm of successive refinement of backlash in the vector requirements

To solve the integer problem of linear cutting proposed algorithms to obtain optimal solution either for the initial vector requirements, or if there is tighter tolerances. Discussed in the Ask the degeneracy of the obtained solutions and numerical results.

XI. Pevnyi A.B., Duriagin A.M. The maximal redundancy of real harmonic frames

The author uses idea from article of M. Püschel, J. Kovacevic and constructs real harmonic frames. They possess the maximal redundancy.

XII. Pevnyi A.B., Istomina M.N., Maksimenko V.V. Construction of equiangular tight frames

Investigate the question of the existence of equiangular tight frame. For the case m = 2n proposed algorithms equiangular tight frames.

XIII. Pevnyi A.B., Kotelina N.O. Lower bound for cardinality of spherical design using linear programming

The theorem of Delsarte for lower bound for cardinality of spherical design and its modification using only even polynomials are given. The corresponding grid problem of linear programming is considered and the results of calculations are given.

Bulletin 13 2011

by

I. Poroshkin A.A., Poroshkin A.G. Three counter-example in analysis

It is represented the examples of the continuous functions on the metric spaces for which the classical theorems of Weierstrass (about boundedness and about achievement of the face) and the theorem of Kantor (about uniformly continuity) are not true.

II. Sidorov V.V. Structure lattice isomorphisms of semirings generated by a one nonnegative function

In this paper we describe isomorphisms of lattices A_{_f} and A_{_g} of all subalgebras with unit of semirings of functions [f] and [g] generated by nonnegative real-valued functions f and g, respectively. It is proved that any isomorphism of lattices A_{_f} and A_{_g} is generated by an isomorphism of semirings [f] and [g]. A techniqe of unigenerated subalgebras is applied.

III. Grytczuk A. On the Diophantine equation x^² – dy^² = z^ⁿ

In this Note we remark that there is some duality connected with the problem of solvability of the Diophantine equation

(*) x² – dy² = zⁿ.

Namely, we prove that the equation (*) has no solution in positive integers x,y for every pime z = q^{^*} generated by an arithmetic progression and for every odd positive integer n if d is squarefree positive integer such that p|d, where p is an odd prime.

IV. Afonin R.E., Malozemov V.N., Pevnyi A.B. Delsarte bounds for the number of elements of the spherical design

The proof of the Delsarte’s theorem for lower bound for cardinality of spherical design is given. The exposition is closed, all auxiliary theorems are proved.

V. Belyaeva N.A., Dovzhko E.S. Model of the formation of spherical products with the nonzero critical depth conversion of the material

The mathematical model of the solidification of the spherical product in the mode of spread of the bilateral front. At the boundaries of the fronts are into account the conditions of coexistence of solid and liquid layers formed products. The results of numerical analysis.

VI. Belyaeva N.A., Kuznetsov K.P. The dissipative structure and domain of anomaly structural liquid Couette flow in a flat clearance

The bifurcation study of structural liquid Couette flow in a flat clearance in the superanomaly area was conducted. Bifurcation diagrams and the values of parameters corresponding to the superanomaly area were obtained. Bifurcation method allowed to obtain an analytical approximation of the stationary inhomogeneous solution in the neigborhood of the bifurcation point. A numerical simulation of the flow was conducted.

VII. Belyayev Yu.N. Wave scattering continuosly stratified elastic media

Method of calculating elements of the second order matrix, which characterizes the elastic continuously layered media is proposed. The representation of reflection and transmission coefficients of the layer through elements of characteristic matrix is given. General solution to the plane wave reflection and transmission in a periodic continuously stratified medium is found.

VIII. Kotelina N.O. Methods of estimating kissing numbers

Methods for estimating of kissing numbers based on linear programming, corresponding grid problems of linear programming and results of calculations in Matlab are given. The table of best known upper bounds for kissing numbers is also given.

IX. Belyaeva N.A., Istomina M.N. Computing System “Bifurcation method in nonlinear models Mechanics”

Computing system includes programs for the branching method in nonlinear mechanics models. The article discusses the general structure of the complex and a description of its constituent programs.

X. Mikhailovskii E.I., Mironov V.V., Podorov V.R. Contact free boundary problem for beams and discrete elastic foundation

The influence of the accounting of transverse shifts on the solution of contact problem for beams and supports of the unilateral action. A generalization to the case of beams, bent on the theory of Timoshenko, the method of enumeration of sets of active supports, based on the proof of the uniqueness of solutions of the nonlinear contact problem and the equations of the analytical version of the so-called theorem of three moments.

XI. Pevnyi A.B., Istomina M.N. A modification of Delsarte’s theorem for the estimation of kissing numbers

A modification of Delsarte’s theorem is proved.

XII. Odyniec W.P. Two hundred years from the date of the birth of the creators of mechanical computers recommended for Demidov Prize H. Slonimsky and H. Kummer

Some materials of the creation of calculating gadgets by H. Slonimsky, H. Kummer and H. Ioffe is considered. In details the Theorem by H.Slonimsky which was the base of these gadgets is presented. This Theorem, devoted to a property of the Farey sequence, is now widely applied in informatics.

XIII. Professor Alexandr Grigiorievich Poroshkin: 60-th year in mathematics and education

XIV.Валерьян Николаевич Исаков (к 65-летию со дня рождения)

Bulletin 14 2011

by

I. Vechtomov E.M., Lubiagina E.N. Lattices continuous function with values in unit segment

In this paper we prove that the lattice of ideals (lattice of congruences) in lattice C(X,[0,1]) dtermines any compactum X. We study the lattice of all continuous [0,1]-value functions on topological spaces X. We proved that any compactum X determined by the lattice of ideals (the lattice of congruences) of a lattice C(X, I). We described the closed ideals of topological lattices C_p(X, I) with the topology of pointwise convergence. We have that a Tikhonov space X defined by the lattice C_p(X, I) as a consequence.

II. Vechtomov E.M., Petrov A.A. Semirings with idempotent multiplication

In this paper we study the structural properties of multiplicatively idempotent semitings. This class of semirings contains all Boolean rings and all kinds of distributive lattices with zero. Particular attention is paid to the finite multiplicatively idempotent semirings and twice idempotent semirings.

III. Mekler A.A. Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, I

In this paper is presented a parallel approach to treating of some invariants of two kinds of classical Banach Function Spaces namely Marcinkiewcz and Orlicz spaces which are denoted M_ψ and L^*_φ, respectively. The exposition has the goal to state that there is such a way of mutually associating into couples (M_ψ, L^*_ψ-) (as well as (M_φ+, L^*_φ)) that isomorphic properties of one of counterpart transfer into they of another one. Moreover by the way the isomorphic properties at ∞ allow to be reduced to ones at 0.

IV. Mekler A.A. Remarks on the correspondence between the topological invariants of spaces, Marcinkiewicz and Orlicz, II

In terms of behavior of limit densities of positive integer sequences an unique interpretation of some topological invariants of Orlicz, respectively, Marcinkiewicz functional spaces (in particular their coincidence) is given.

V. Nikitenkov V.L., Kholopov A.A. The exact formulae for the optimal parameters of ASM

An additive-split method (ASM) is used for solving an equation x=b-Ax in a Banach space with linear operator A. The exact formulae for the optimal parameters of ASM which extend mostly the real spectral interval of convergence are given.

VI. Belyaeva N.A., Stepanova A.S. Flow of viscous structure fluid among two cylinders

Presents the second part of the article (the first part was published in the [1]) devoted to the impact assessment transient viscosity on flow map of incompressible structure fluid among two cylinders with swirl. The state [1] analyzestationary axial flow of incompressible fluid with constant viscosity, it present numerical solution and checking findings with theretical research was presented in [2-4], where vortex deduced analytically by method solution determination in view of polynoms.

VII. Yermolenko A.V. A variant of the refined theory of flat plates for the solution of contact problems

Using the method of generalized reaction it was obtained the solution of contact problem for an axisymmetric circular plate and an absolutely rigid base. In addition the solution was obtained with using the Karman-Timoshenko-Naghdi type equations, which were given to the lower surface of the plate.

VIII. Belyaeva N.A., Kamburov D.M. Computing System “Solid-phase extrusion”

Computing system combines algorithms and software modules for calculating the parameters of viscoelastic flow of a compressible structured composite material in the solid-phase extrusion, developed at the Department of Mathematical Modelling and Cybernetics of Syktyvkar State University.

IX. Belyaeva N.A., Khudoyeva E.E. Computing complex “Thermoviscoelastic models of the formation of axisymmetric products”

The computing complex integrates series of programs developed within the mathematical models of the formation of axisymmetric products (cylinder, sphere) in the process of their obtaining in the parallel reactions of polymerization and crystallization. The article gives a description and operating principles of the complex.

X. Vasiliev A.A., Nikitenkov V.L., Kimask K.V., Malkov S.V. Internet-version course of mathematics for nonmathematical specialities (with chapters from elementary mathematics)

The Internet-version (current) course of mathematics for nonmathematical specialities (with chapters from elementary mathematics) is described.

XI. Nikitenkov V.L, Bayborodina O.V., Poberii A.A. Generalization algorithm packing sliced rolls

In this article considered generalization problem packing sliced rolls, that is consider in article [10]. Now we shall look at situation not only one diameter, but several diameters and problem of overspending would solved not by adding new formats packing paper (PP), it would solved by changing current formats by others, which would give us lesser overspending.

XII. Vasiliev A.N., Gintner A.N. Two approaches to the solution of one classical problem of computational geometry

In this work consider problem of finding the largest empty circle and the smallest covering circle. The implementation of algorithms for solving these problems by using methods of computational geometry, in particular of Delaunay triangulation and its dual Voronoi diagram is discribed. In the work also performed numerical experiments and graphically presents results of problems.