VESTNIK Syktyvkar University. Ser. 1.
Mathematics, Mechanics, Informatics.
№ 15 2012

ARTICLES

• Belyaeva N.A., Pryanishnikova E.A. Mathematical modeling in the extrusion
  
  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 in the joint consideration of Reo-Dinamics, kinetics of structuring and temperature factor.
  
  Keywords: extrusion, composite material, Reo-Dinamics, structurization, heat exchange.
  
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• Yermolenko A.V. On analytical solution of the contact problem
  
  Analytical solution for a cylindrically bending plate and a rigid foundation was obtained with using the Karman-Timoshenko-Naghdi type equations, which were given to the lower surface of the plate.
  
  Keywords: theory of plates, contact problem, analytical solution.
  
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• Malozemov V.N. On the fortieth anniversary of MDM-method
  
  MDM-method (Malozemov-Demyanov-Mitchell method) is used for the finding the point of a polyhedron which is closest to the origin. The polyhedron is defined as the convex hull of the given points in n-dimensional space.
  
  Keywords: point of a polyhedron which is closest to the origin, interative procedure, computing the minimum, quadratic form.
  
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• Tarasov V.N., Andryukova V.Yu. On stability behavior of a toroidal shell with a one-sided reinforcement
  
  The axisymmetric problem of stability of the toroidal shell that is subjected to external normal pressure is considered. For calculation of work of external forces the exact formula is used. In this paper the variational approach is applied, for a finite-dimensional approximation cubic splines are used. The influence of nonlinear terms caused by unilateral contact with an elastic filler on the value of critical force is investigated.
  
  Keywords: toroidal shell, stability, cubic splines, one-sided contact, the critical force, the variational problem.
  
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• Vechtomov E.M., Lubiagina E.N. Semirings of sc-functions
  
  In this paper we consider the semiring SC(X, I) of [0,1]-valued functions on a topological space X, which are sharp upper bounds of sets of continuous functions. We have established a duality between the category of Tychonoff spaces X with continuous maps and the category of semirings SC(X, I) with complete homomorphisms as morphisms.
  
  Keywords: semiring, topological space, upper bounds.
  
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• Golovneva E.V. A class of matrices with diagonal domination
  
  The article is devoted to a special class of real valued matrices with diagonal domination. This class is of considerable importance for the theory of homogeneous Markov processes with continuous time and discrete state space.
  
  Keywords: determinant, Markov process.
  
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• Grytczuk A. Ankeny, Artin and Chowla conjecture for even generators
  
  In the paper [2] Ankeny, Artin and Chowla conjectured that if p is a prime such that p≡1(mod 4) and ε = (t+u√p)/2 is the fundamental unit of the real quadratic field K = Q(√p) then p|u.
  
  In this paper we prove that this conjecture is true for even generators t, u of the fundamental unit ε.
  
  Primary subjects: 11 A 55, 11D 09
  Secondary subjects: 11 R 11
  
  Keywords: generators, prime numbers, diafantic equation.
  
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• Mekler A.A. On Marcinkiewicz modulars on [0,1] and [0,∞)
  
  It is presented a reduction to one-another of two cases: the case of Marcinkiewicz (Lorenz, Orlicz) functional spaces on the unit interval and the case of the same spaces on the positive semiaxis. In this connection p-convexity of these spaces is discussed.
  
  Keywords: symmetrical Marcinkiewicz modulars, equiconcave pseudopower functions.
  
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• Mironov V.V., Mayborov A.S. The method of nonlinear integral equations in the problem of bending of a closed cylindrical shell with rigidly clamped edges
  
  Work is devoted to definition intense the deformed conditions in a selfcontained cylindrical envelope under the influence of normal loading. As constitutive equations of equilibrium the equations of a bend of cylindrical envelopes are taken such as the Pocket. In the theory of the non-linear equations of the Pocket the routinely droppable is considered Λ(ψ,ω) item.
  
  The boundary value problem is solved, recognizing that initial loading is evenly the distributed on a platform which sizes are proportional to the sizes envelopes (in expanded form) and which center coincides with the center of an envelope. The envelope is hardly jammed on both edges. The solution of a task is consolidated to finding of a deflection and stress functions. The main idea is replacement integro-differential set of equations on integral system (a method of non-linear integral equations) which decides concerning the second derivativ required functions of a deflection and tension. For its permission it is used Richardson's stationary method, and also replacement of integrals by ranks with the help quadratures of Legendre.
  
  The main feature of this work is finding of a Green function biharmonic operator Maurice Levi's method. The second feature consists in that in Richardson's stationary method the various can be used parameters which are responsible for speed of convergence for deflection and a stress function, at the expence of what it is possible to increase speed of convergence of a repetitive process.
  
  Keywords: stress-strain state, a closed cylindrical shell, the equation of von Karman type.
  
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• Nikitenkov V.L., Jidkova O.A., Shekhurdina E.S. The boundaries of finding the critical force in the environment multimodulus
  
  The results obtained in [1] for the case multimodulus environments.
  
  Keywords: critical load, stiffness, medium, medium multimodulus.
  
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• Popova N.K., Ogirchyik T.A. 3D animation and simulation of an object with Autodesk 3ds Max 2009
  
  In given article the process of animation of the three-dimensional charater is described. As the character a brown bear, the symbol of the city Syktyvkar, has been chosen. Simulation was required to study exterior and movement of the character, to create three-dimensional object, to execute object animation.
  
  Keywords: three-dimensional object, animation.
  
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• Odyniec W.P. Returing to H. Kummer
  
  Some new materials of the inventor of calculating gadgets H. Kummer's biography including the date of his death are considered.
  
  Keywords: calculating gadgets, H. Kummer.
  
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• Порошкин А.А., Порошкин А.Г. Три контрпримера в анализе
  
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