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Sibirskii Zhurnal Industrial'noi Matematiki
2009, vol. 12, No 4 (40)
Contents
UDC 519.24:336.71
Artem’ev S. S., Prokaeva M. N., Fedorov A. A.
The Statistical Modeling of Insurance for the Credit Risk of a Bond PortfolioWe study statistical modeling algorithms for bond default times in a portfolio with various interdependencies, as well as algorithms for computing the amount of the credit default swap coupon. Considering the distribution of the bond portfolio owner's earnings or losses with and without insurance, we present the results of some numerical experiments.
Keywords: bond default time, credit default swap, insurance coupon size, earnings/losses distribution, statistical modeling.
Pp. 3–11.Artem’ev Sergey Semenovich
Institute of Computational Mathematics and Mathematical Geophysics, 6, Acad. Lavrent’ev prospect, Novosibirsk State University, E-mail: ssa@osmf.sscc.ru
Prokaeva Marina Nikolaevna, Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk, E-mail: promar@yandex.ru
Fedorov Alekseui Aleksandrovich
Novosibirsk State Technical University, 20 Karl Marx prospekt, 630092 Novosibirsk, E-mail: New_Okela@mail.ru
UDC 517.1:512.816
Bogdanova R. A.
The Groups of Motions of Two-Dimensional Helmholtz Geometries as Solutions to Functional EquationsWe consider the problem of finding the local groups of all motions of two-dimensional Helmholtz geometries, which reduces to solving functional equations.
Keywords: phenomenologically symmetric geometry, the group of motions, functional equation.
Pp. 12–22.Bogdanova Rada Aleksandrovna
Gorno-Altauisk State University 26 Socialisticheskaya str. 649000 Gorno-Altauisk. E-mail: bog-rada@yandex.ru
UDC 519.86
Vasil’ev V. A., Suslov V. I.
On Unblockable States in Multiregional Economic SystemsWe study conditions for the existence of unblockable states in a class of models considered in a series of articles on multiregional economic systems. We describe cooperative games associated to these models and reduce some questions of coalition stability of regional development plans to the corresponding problems of game-theoretic analysis. Using the classical Scarf core nonemptiness theorem for cooperative games, we establish sufficiently simple conditions for the existence of unblockable states in the models of interregional economic interaction in question. Important roles in the implementation of our approach belong to the linearity of the models considered and the ensuing polyhedrality of the sets of balanced plans of regional coalitions.
Keywords: model of a multiregional system, unblockable state, cooperative game, core, balanced game, polyhedral set.
Pp. 23–34.Vasil’ev Valery Aleksandrovich
Sobolev Institute of Mathematics, 4 Acad. Koptyug prospect, E-mail: vasilev@math.nsc.ru
Suslov Viktor Ivanovich
Institute of Economics and Industrial Engineering, 17 Lavrent’ev prospect, 630090 Novosibirsk, E-mail: vasilev@math.nsc.ru; suslov@ieie.nsc.ru
UDC 517.91
Gorban’ A. N., Cheresiz V. M.
Slow Relaxations and Bifurcations of the Limiting Sets of Dynamical Systems. III. Slow Relaxations of a Separate Semi-FlowWe study the relations of various types of slow relaxations of a dynamical system to its specific behavior both in the general situation, when the phase space of the system is an arbitrary compact metric space, and in the case that it is a smooth manifold which is particulary useful in applications.
Keywords: one-parameter semigroups of homeomorphisms, slow relaxations, bifurcations of limiting sets.
Pp. 35–43.Gorban’ Aleksandr Nikolaevich
Institute of Numerical Modeling, Akademgorodok, 660036 Krasnoyarsk,
Leicester University, United Kingdom, E-mail: ag153@leicester.ac.uk
Cheresiz Vladimir Mikhauilovich
Sobolev Institute of Mathematics, 4 Acad. Koptyug prospect, 630090 Novosibirsk
UDC 519.17
Dobrynin A. A.
The Wiener Index for Graphs of Arbitrary Girth and Their Edge GraphsWe consider the invariant W(G) (Wiener index) of a simple connected nondirected graph G, which is equal to the sum of distances between all pairs of vertices in the natural metric. We show that for every g ³ 5 there exist planar graphs G with a shortest cycle of length g for which W(L(G)) = W(G), where L(G) is the edge graph for G.
Keywords: invariant graph, distance in graphs, Wiener index.
Pp. 44–50.Dobrynin Andreui Alekseevich
Sobolev Institute of Mathematics, 4 Acad. Koptyug prospect, 630090 Novosibirsk, E-mail: dobr@math.nsc.ru
UDC 517.95
Kazakov A. L.
The Generalized Cauchy Problem for a Quasilinear System with Two SingularitiesWe consider the generalized Cauchy problem with data on two characteristic surfaces. We prove an existence and uniqueness theorem for solutions to problems in the class of analytic functions.
Keywords: partial differential equations, quasilinear system, initial-boundary value problem, analytic solution, series, convergence, majorant.
Pp. 51–64.Kazakov Aleksandr Leonidovich
Institute of Dynamical Systems and Control Theory, 134 Lermontova str. 664033 Irkutsk, E-mail: kazakov@icc.ru
UDC 517.9
Kozhanov A. I.
On the Solvability of Boundary Value Problems for the Quasilinear Ultraparabolic Equations of Certain Mathematical Models of the Dynamics of Biological SystemsWe consider the problem of modeling population dynamics. Mathematically this problem reduces to studying the solvability of a nonlocal boundary value problem for a quasilinear ultraparabolic equation with astronomic time t and biological time a (the age). In the problem under study we prove the existence and uniqueness theorem for regular solutions.
Keywords: population dynamics, nonlinear ultraparabolic equation, nonlocal boundary value problem, existence of solutions, properties of solutions.
Pp. 64–78.Kozhanov A. I.
Sobolev Institute of Mathematics, 4 Acad. Koptyug prospect, 630090 Novosibirsk, E-mail: kozhanov@math.nsc.ru
UDC 51-76:581.5
Kolobov A. N., Frisman Ye. Ya.
Modeling Competitive Interaction in Tree CommunitiesWe propose a mathematical model describing the growth and interaction of trees as a result of competition for light. We analyze quantitatively the behavior of the model for various parameter values. We show that for certain variations of parameters the species either coexist or displace each other. We note the relation between tree sizes and their density. The results of the verification of the model show a sufficiently high precision of the approximation by the calculated curves to the data gathered at the regular test areas of the Bastak Nature Reserve.
Keywords: modeling, competition, photosynthesis intensity, tree community.
Pp. 79–91.Kolobov Alekseui Nikolaevich
Frisman Efim Yakovlevich
Institute of Complex Analysis of Regional Problems, 4, Sholom Aleyhem St., 679016 Birobidzhan E-mail: carpi@yandex.ru
UDC 517.95
Neustroeva N. V.
Rigid Switching in the Contact Problem for Elastic PlatesWe consider a family of problems describing the contact of elastic plates located at a fixed angle to each other and, in the natural state, touching along a line. The plates are subjected only to bending. We study passage to the limit from elastic switching to rigid switching. We show that the limiting problems describe exactly the contact of an elastic plate with a rigid bar and the problem of the equilibrium of an elastic plate with rigid switching. We establish the solvability of the problems; find the boundary conditions holding on the possible contact set and their precise interpretation.
Keywords: Kirghoff–Lyav model, contact problem, rigid switching.
Pp. 92–105.Neustroeva Natalia Valerianovna
Institute of Mathematics and Informatics, Yakutsk State University, 58 Belinskiui str., 677000, Yakutsk, E-mail: NNataliaV@mail.ru
UDC 517.946:550.837
Persova M. G., Soloveuichik Yu. G., Abramov M. V.
Finite Elements Modeling of Geoelectromagnetic Fields Excited by a Horizontal Charged RodWe apply the finite elements method to modeling the electromagnetic field excited by a horizontal rod with electric current, in order to solve geoelectric surveying problems. We present computational schemes for computing the electromagnetic field in the ambient horizontally layered medium and a medium with 3-dimensional objects. We analyze the computational efficiency of the approach.
Keywords: numerical 3D-modeling, electromagnetic field, geoelectricity problems, horizontal rod, finite elements method.
Pp. 106–119.Persova Marina Gennad’evna
Soloveuichik Yuri Grigor’evich
Abramov Mikhail Vladimirovich
Novosibirsk State Technical University 20 Karl Marx prospect, 630092 Novosibirsk, E-mail: persova@fpm.ami.nstu.ru
UDC 532.582
Sennitskiui V. L.
On the Effects of Equilibrium and Cyclic Frequency Oscillations of a Solid in a FluidWe consider the problem of torsional oscillations of an inhomogeneous solid of an arbitrary smooth shape in an ideal fluid in the presence of gravity. We discover new hydromechanical effects: as a result of the mass redistribution of the solid, the stable equilibrium state of the solid changes, while the cyclic frequency of its oscillations is preserved, and conversely, the cyclic frequency of oscillations of the solid changes, while its stable equilibrium state is preserved.
Keywords: fluid, solid, equilibrium state, oscillations, cyclic frequency.
Pp. 120–127.Sennitskiui Vladimir Leonidovich
Lavrent’ev Institute of Hydrodynamics, 15 Acad. Lavrent’ev prospect, 630090 Novosibirsk, E-mail: igil@hydro.nsc.ru
UDC 533:517.958
Tarasova Yu. V.
The Classification of Submodels with a Linear Velocity Field in Gas DynamicsWe seek a solution, as a linear velocity field, to the equations of gas dynamics with an arbitrary state equation. We classify the submodels according to the state equations in the case that the auxiliary matrix is nondegenerate.
Keywords: gas dynamics, state equation, linear velocity field.
Pp. 128–136.Tarasova Yulia Valer’evna
Ufa State Aviation Technical University, 12 Karl Marx str., 450000 Ufa, E-mail: taryv@yandex.ru
UDC 330.115
Trubacheva A. E.
On Optimality of the Flat Proportional Tax Rate in a Two-Level Economic SystemWe study the functioning of an hierarchical system: the state—an investor (enterprise head)—manufacturing. For the system with various manufacturing functions we simultaneously solve the following two problems. For the investor we solve the consumption-investment problem, and for the state, the problem of increasing the tax collection. We prove a turnpike theorem on the optimal value of the investment part for the lower level of control in the two-level problem with flat proportional taxation. We give examples showing that there exists a situation for which the two-level problem of tax rate optimization has a nontrivial optimal solution.
Trubacheva Anna Evgen’evna
Sobolev Institute of Mathematics, 4 Acad. Koptyug prospect, 630090 Novosibirsk, E-mail: aetrub@math.nsc.ru