
The problem of complex meaning nonlinear equation in quotiend derivatives
Several ways of finding of the exact solutions inherent in the equations with soliton like solutions were applied to the given equation. In particular the presence of property of Penleve in the equation was conducted, solutions in the form of numbers of Lorana, exact solutions in the form ...

An impacton solution for the vortex filament
A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: ...

The dynamics of localized pulse as solutions of Davey — Stewartson II equations
A class of spatially localized solutions of Davey — Stewartson II equation is examined; it is shown that such solutions tend to lose the locality properties with time scale corresponding to a characteristic space scale of initial localization. The locality loss manifests itself with ...

A surprising tale of longperiodic spin oscillations in the synthetic antiferromagnets: some exact solutions
... collisions between the magnetic domains of different spin orientations ( and ). The resulting model comprised of a system of nonlinear differential equations is closely examined, after which we propose a simple analytical method of construction of its exact solutions. This method is shown to generate an infinite family of solutions associated with the degenerate hypergeometric functions, parameterized by a natural number N. One of those solutions with N = 2 produces the magnetization function which perfectly ...

Numerical solution of the Schrödinger equations with polynomial potentials (Part II)
The algorithm of the numerical realization of a fundamental solution of a Cauchy problem for the onedimensional Schrodinger equation with polynomial potentials is described. The stationary Schrodinger equation for a proton in the double potential well is solved by using Ritz variation method. The Green’s function ...

One method for constructing exact solutions of equations of twodimensional hydrodynamics of an incompressible fluid
We propose a simple algebraic method for constructing exact solutions of equations of twodimensional hydrodynamics of an incompressible fluids.The problem reduces to consecutively solution three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations ...

Generation of exact solutions of Fridman equations leading to Cardy–Verlinde formula by Darboux transformation
It is considered a possibility of generation of exact solutions for Friedman equations by Darboux transformation, for which Cardy — Verlinde formula is valid. Two modifications of Darboux transformation are offered, which let generate such solutions. Exact solutions are obtained, for which Cardy — Verlinde ...

The new procedure of receiving the multisoliton solutions of the KdV equation
The article offers a new method of obtaining multisoliton solutions of KdV equations by means of introducing the characteristic polynomial.
The authors form a representation for multisoliton solutions through the second logarithmic derivative of a determinant of a positivedefinite matrix.
1.
Захаров ...

On a 3D visualization of a solution to the problem of top movement along a smooth horizontal surface
This article considers the problem of 3D visualization of two examples of top movement along a smooth surface. The authors analyze the cases where analytical solutions are possible. Graphical illustrations to these solutions are provided.
1. Голубева О. В. Теоретическая механика. М., 1961.
2. Суслов Г. К. Теоретическая механика. М., 1944.
3....

An application of the Abel equation of first type to the task of solving the Friedman equations
An interesting connection between EinsteinFriedmann equations for the models of universe filled with scalar field and the special form of Abel equation of the first kind is presented. In particular, it is shown how, knowing the general solution of the Abel equation (corresponding to the given scalar field potential) one can obtain the general solution of the Friedmann Equation.
1.
Abel
N.
H.
Oeuvres Complétes II. S. Lie and L. Sylow, Eds., Christiana, 1881.
2.
Appell P. ...

A Lax pair for the (1+3) nonlinear equation
... physics. The discovery of inverse scattering method played an important role in reconsidering the place of integrable systems of nonlinear partial differential equations in mathematical sciences. The search for a systematic approach to developing exact solutions of such systems has become one of the main problems in the theory of integrable systems.
1. Fokas A. S. Symmetries and integrability // Stud. Appl. Math. 77. 1987. No. 3. P. 253—299.
2. Солитоны и метод обратной задачи ...

New classes of exact solutions and consistent models of cosmological evolution
A method for construction of exact cosmological solutions of Einstein equations is developed. The method is based on representation of these equations as a secondorder linear differential equation. Particularly, the method allows to construct a more general solution, parametrized by two constants,...

1+1Dimensional Yang — Mills Equations and Mass via Quasiclassical Correction to Action
...
9. Brüning J., Grushin V. V., Dobrokhotov S. Yu., Tudorovskii T. Ya. Generalized FoldyWouthuysen Transformation and Pseudodifferential Operators // Theor. Math. Phys. 2011. Vol. 167, iss. 2. P. 171—192.
10. Leble S. Quantum Corrections to Static Solutions of Nahm Equation and SinGordon Models via Generalized ZetaFunction // Theor. Math. Phys. 2009. Vol. 160, iss. 1. P. 976—985.
11. Boozer A. D. Classical YangMills theory // Am. J. Phys. 2011. Vol. 79, iss. 9. P. 925—931.
12. Leble S. Quantum ...

Application the theory of an optimum detection for a spatial resolution of signals
The article deals with application of the theory of optimum detection to the azimuth resolution of two sound sources. This paper compares the solutions based on maximum likelihood method with the classical approach (Rayleigh's approach). Furthermore, the computer model and the testbench (experimental apparatus) have been created for an extensive analysis of the obtained solution. Our experimental ...

A solution of the transport task in relation to the cargo rail transportation
A task of searching of the optimal route maximizing the carrier profits is formulated. А сomparison of several methods of this task solution is carried out.
1. Balas E., Martin G. ROLLAROUND: Software Package for Scheduling the Rounds of a Rolling Mill. Pittsburgh, PA, 1986.
2. Fischetti M., Toth P. An additive approach for the optimal solution of the prizecollecting travelling ...

Numerical solution of the linearized inverse problem for acoustic equation
In this paper we develop an algorithm of numerical solution of the inverse dynamical problem about speed of sound reconstruction in horizontally layered acoustical medium. The solution is based on linearized version of the Boundary Control Method. The inverse data is the response at the single boundary ...

Ill Posed Problems and Information Security
Well posed (by Hadamard) problem has properties of existence, uniqueness and stability of its solution. Ill posed problems do not have at least one of the above properties, often this is the stability property of the solution with respect to initial conditions. The solution of such problems is sensitive even to a small change in the values of ...

Set of algorithms for constructing university timetable — part 2: Data presentation structure and algorithm for building a base solution
An algorithm for building a base multitude of solutions for the university timetabling problem is proposed. An algorithm allowed to get at least one correct timetable if such exists. Computational complexity is reduced with using a special set of heuristics and timetable data presentation model.
...

Exultonlike solution and two phase of collapse of an intrusive lens
We show that it is possible to use the exultonlike solutions of the nonlinear Schrődinger equation to simulation of the evolution of frontal vortical zone of an intrathermocline eddies in the process of its collapse.
1.
Гриценко В.
А., Юрова А.
А.
К вопросу о динамике ...

The Abel equation and cosmological scalar field zeroes
This article presents a new simple analytical method that makes it possible to design solutions in describing the dynamics of the universe near the zeroes of the scalar field potential.
1. Yurov V. А. An application of Abel’s equation of first kind to the search of solutions of Friedman’s equations // Вестник РГУ им....

Numerical solution of the Schrödinger equations with polynomial potentials (Part I)
The fundamental solution of a Cauchy problem and the spectral task for a onedimensional Schrodinger equations with potential in the form of polynomials m P (x) (m 6) is solved. Numerical calculations are applied to modelling adiabatic potentials with two minima ...

An analysis of heterogeneous thinking techniques and the prospects for their implementation by hybrid intelligent multiagent systems
In this article, we consider techniques for, and approaches to, the organization of various stages of heterogeneous solution design in small expert teams. Simulating the heterogeneous design of team solutions by hybrid intellectual multiagent systems will contribute to the efficiency of problemsolving in dynamic environments. We propose a structure of a hybrid intelligent ...

The solution of a problem of detection of a signal at vertical sounding of an ionosphere
In the real work the solution of a problem of determination of parameters of the radio impulse reflected from an ionosphere is considered. The noise component, and also the multibeam structure of a signal arising at formation two magnetoionic component is thus considered....

Environmentally safe growth stimulator for presowing seed treatment
This article examines the influence of a presowing seed treatment with a hydrogen peroxide and potassium permanganate solution on the germination, seedling growth, and average weight of the fruit of Lycopersicum esculenum. An increase in seed germination, the average weight of fruit, and resistance to adverse weather conditions and diseases and more active growth of ...

The strategic potential of an organisation and the models of programming solutions in the conditions of uncertainty
This article considers the problems of studying the strategic potential of organisations in the modern conditions. The authors analyse the methods of allowing for the uncertainty factor within the programming solution development procedures.
1. Друкер П. Ф. Задачи менеджмента в XXI веке / пер. с англ. М., 2004.
2. Нельсон Р., Уинтер С. Эволюционная теория экономических ...

Threedimensional computational modelling of water cooling over the coastal slope: a comparison of hydrostatic and nonhydrostatic solutions
This article addresses the structure and dynamics of current and temperature fields in the coastal zone of a large water body generated by seasonal variations of heatexchange conditions at the water surface. Numerical solutions of threedimensional hydrostatic and nonhydrostatic models MIKE3FlowModel in shallow and deep parts of the basin are compared. It is shown that the structure of fields is reproduced adequately by both models and water currents are similar; ...

Nonlinear dissipative structures as model of twodimensional optic solitons
... transformations for the Boiti — Leon — Pempinelli equations (BLP). These equations are the (1+2) generalization of the sinhGordon equation. In addition, the BLP equations reduced to the Burgers equation in a onedimensional limit. Localized nonsingular solutions in both spatial dimensions and anti ”blowup” solutions are constructed.
1. Boiti M., Leon J. J.P., Pempinelli F. Spectral transform for a two spatial dimension extension of the dispersive long wave equation // Inverse Problems. 1987....

An integrable case of the Schrödinger matrix equation for multilevel quantum systems
Explicit solutions of the Schrödinger matrix equation are received and performed the calculations of the main invariants. It is established that the characteristic equation in all cases has only 2 roots, one is a simple and second is multiple.
1.
Зайцев ...

The relations for potentials of filtration flows in media with common boundary and there employing for founded solutions some problems
The structure of filtration flows in twodimensional laying media is studied. The definition of positive and negative flows is giving. The relations for complex potentials in media with common boundary are receiving. There are employing for founded solutions some problems.
1. ПолубариноваКочина П. Я. Теория движения грунтовых вод. М.,1977.
2. Голубева О. В. Курс механики сплошных сред. М., 1972.
3. Голубева ...

The impact of changes in dissolved organic carbon concentration in a solution on the sorption of platinum compounds
This article considers the impact of changing dissolved organic carbon concentration in a solution on the sorption of platinum (II), (IV) compounds (K2PtCl4, H2PtCl6) at different soil horizons. The authors prove that even small concentrations of dissolved organic carbon play an important role in platinum sorption in soil and background minerals....

Modeling of Wave Processes in High Speed Impacts with Smoothed Particle Hydrodynamics Method
Concerned issues are related to the modeling of high speed impact with different variants of the smoothed particle hydrodynamics method and applying this method to the solution of problems of mechanics of the deformed solid body.Results of solution of the problem of disintegration of discontinuity were obtained and comparative analysis was performed.
1.
Monagan J. J.
An introduction to SPH // Comput. Phys
.
Comm
...

Cyclic version of “ – ” iterative method. Estimations of speed of algorithm convergence
Differences methods of the approximate solution of the twodimensional equation of ions diffusion with the mixed derivatives and the first derivatives of a divergent look are considered. Test calculations on a modeling task with the known analytical decision are carried out. Operability of ...

Oscillations, resonances and waves in a nonlocal medium with sources
New exact solutions are obtained for a spatially nonlocal wave equation with sources. The results are set out in the terms of the heat transfer theory. The nonlocality of the problem is determined by the value of the fourth spatial derivative. We considered two ...

The structural–dynamic model of tolerancebased solutions of pedagogical problems
... педагогической толерантности у будущих учителей: дис. … канд. психол. наук. Волгоград, 2004.
Lopushnyan G.
teacher's tolerance, pedagogical model, pedagogical problem, tolerancebased solution of a pedagogical problem.
147155

Bases of the theory of digital communication systems with not orthogonal carrier frequencies
The algorithm of the solution of the task of permission of signals in communication systems with not orthogonal carrier frequencies is provided. A basis are provisions of the theory of optimum reception in the annex to communication systems. It is shown that the system of ...

To the question of control of accuracy in solving the inverse problem microseismic
... solving the inverse kinematics problem of microseismic. This problem is to determine coordinates of acoustic emission sources. Investigate questions of constructing optimal algorithms and the influence of noise in the data on the stability of the obtained solution. Demonstrate the effectiveness of this approach in comparison with generic algorithms without estimation of optimal parameters of the solution.
1. Erokhin G. N., Bortnikov P. B. Inverse problem of determination of the earthquake source seismic ...

The filtration radio pulse maximum likelihood method
This article presents a solution to the problem of resolution of two radio impulses through the maximum likelihood method. The authors have obtained expressions for the optimum processing of a set of two radio impulses in the domains of their orthogonality and nonorthogonality,...

GMOs in agriculture: legal regulation and discussion
... still no unanimous opinion of the effects produced by GMOs. Given the uncertainty, the ban on the use of genetic engineering in agriculture leads to the weakening of the role of legislation as a regulator of public relations. The authors suggest legal solutions to this problem striking a reasonable balance between the interests of business, society and state.
1. Информация о решении ЕСПЧ от 29.06.2010 по делу «Юбер Карон и другие (Hubert Caron and Others) ...

Foreign economic activity of Saint Petersburg, the Leningrad Region, and the Republic of Karelia: problems and opportunities for development
... cluster of regions formed by the city of St. Petersburg, the Leningrad region and the Republic of Karelia. All three areas face a number of challenges when it comes to international trade: challenges that are shared and that require strategic coordinated solutions from regional decisionmakers. One of such solutions, for example, could require pooling of competitive advantages of these areas. The analysis of strategic documents of regional development, however, shows that the issue of interregional cooperation ...

On the relations between the integrable hierarchies
... 1. С. 146—153.
8. Yurov A. V. Closed dressing chains of D = 1 and D = 2 Toda lattice // Dynamics of PDE. 2004. Vol. 1, № 2. P. 85–89.
9. Dubard P., Gaillard P., Klein C., Matveev V. On multirogue wave solutionsof the NLS equation and positon solutions of the KdV equation // Eur. Phys. J. Spec. Top. 2010. Vol. 185. P. 247–258.
10. Yurova A. A. A hidden life of Peregrine's soliton: rouge waves in the oceanic depths // Int. J. Geom. Methods Mod. Phys. 2014. Vol. 11. Р. 1450057.
11. Юров ...

Numerical simulation of forming and evolution of solitons in chain of nucleotide couples
... charge movement along the discrete chain of nucleotide couples in DNA is solved in the frame of Holstein’s model taking account surrounding temperature fluctuations. For the initial conditions chosen specifically the evolution of a special class of solutions of this problem related to the type of soliton is investigated. The existence of solutions in the form of solitary waves in the framework of this model is possible only at very low temperatures the thermostat.
1. Lakhno V. D. DNA nanobioelectronics ...

Formal Languages and Automata VI:algebraic systems and transducers
... quemirings generalizing the classical contextfree grammars generating languages overnite and innite words. The presentation of these results is based on continuous starsemiringomegasemimodule pairs. We dene !algebraic systems and characterize their solutions
of order k by behaviors of algebraic nite automata. These solutions are then set in correspondence to !contextfree languages. Then we introduce rational and algebraic transducers, and abstract !families of power series over quemirings and ...

Local SelfGovernment: Problems of Territorial Administration and Hierarchisation
This article is dedicated to the problem of zoning at the level of local administration. The author determines and analyses the main complications arising at the determination of municipality borders and offers solutions to these problems.
Sharygin M.
local administration, territory, populated place, municipalities
5153

The Flow of Gas with Dispersed Particles in a Cylindrical Channel at a Subsonic Speed
... the gas. The problem of identifying the dynamic characteristics of dispersed particle containing inert gas feed into ladles and the converter is used to improve the accuracy of inert gas dosing. The relevant boundary value problem has no analytical solution. We consider the dynamics of a steady flow of a perfect gas containing dispersed particle in a vertical channel. Numerical methods are used to obtain a solution to the boundary value problem in the Mathcad environment. We present the results ...

On ensuring the energy security of the Kaliningrad region
... possibilities for minimising energy threats to the economy of the Kaliningrad region — an isolated Russian exclave. The authors consider the key aspects of the region’s economic security, identify threats, and provide a critical assessment different solutions to this problems. The research is based on the data of Rosstat and international statistics (IEA), analytical materials, and publications on the problems of global and regional energy security.
The articles suggests that the optimal solution ...

The Swedish model of spatial planning: Functions, problems, and solutions
... development plan, Special area regulations and Property regulation plan. Particular attention is paid to the influence on the planning process of the entry of Sweden to the European Union. The problems associated with spatial planning are made evident and solutions are proposed. Swedish experience may be interesting to the urban and regional planners.
1. Чистобаев А. И., Красовская О. В., Скатерщиков С. В. Территориальное планирование на ...

The first Stokes method in the problem of waves on a liquid surface of finite depth
An approximate solution of the problem of the structure and characteristics of a stationary nonlinear periodic wave on the surface of a liquid of finite depth has been obtained. The solution is as follows: first, the kinematic and dynamic conditions are simplified....

The dynamics of chiral cosmological fields in the canonical phantom model
... potential fields of cooperation remains constant (as seen in the model of the "new" inflation). We present a general algorithm for solving dynamic equations on chiral (scalar) fields and examine special cases when it is possible to find a solution in elementary functions.
1. Ade P. A. R., Aghanim N., Arnaud M. et al. (Planck Collaboration). Planck 2015 results. XIII. Cosmological parameters // Astron. Astrophys. 2016. Vol. 594. URL:
https://arxiv.org/pdf/1502.01589.pdf
(дата ...

The justification of legal punishment in Kant’s philosophy
... as retributivist? While acknowledging the significance of this question the author stresses a more fundamental one lying behind it: Is a noncontradictory theory of punishment conceivable at all within Kant’s philosophy? It is demonstrated that a solution of this question largely determines a justification of the doctrine of right as such as well as a solution of the problem of relation between right and ethics in Kantian philosophy. Some recent interpretations of Kant’s theory of punishment ...

Possible applications of the resources of the Mathematica programming environment to solving mathematical problems
... automatic control of initial data input, input data generator, and a means to improve the visibility of mathematical problem solving. The author offers examples of Mathematica codes for each case and identifies the sequence of stages of displaying the whole solution process by means of Mathematica.
Ivanova N.
Mathematica development environment, input data control tool,
data generator, visibility increase tool.
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