A. Polyanin

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Handbook of First-Order Partial Differential Equations

A. Polyanin, V. Zaitsev, A. Moussiaux, 2001 .

Handbook of Linear Partial Differential Equations for Engineers and Scientists

A. Polyanin, 2001 .

Handbook of Nonlinear Partial Differential Equations

A. Polyanin, V. Zaitsev, 2003 .

Handbook of Integral Equations: Second Edition

Andrei D. Polyanin, Alexander V. Manzhirov, A. V. Manzhirov, 2008 .

Handbook of mathematics for engineers and scientists

A. V. Manzhirov, A. Polyanin, 2006 .

Application of non-local transformations for numerical integration of singularly perturbed boundary-value problems with a small parameter

A. Polyanin, I. Shingareva, 2018, International Journal of Non-Linear Mechanics.

Polyanin, A. D. and Zaitsev, V. F., Handbook of Nonlinear Partial Differential Equations , Chapman & Hall/CRC, Boca

Andrei D. Polyanin, A. Polyanin, 2004 .

Differential-difference heat-conduction and diffusion models and equations with a finite relaxation time

A. Polyanin, A. Vyazmin, 2013, Theoretical Foundations of Chemical Engineering.

Decomposition of three-dimensional linearized equations for Maxwell and Oldroyd viscoelastic fluids and their generalizations

A. Polyanin, A. Vyazmin, 2013, Theoretical Foundations of Chemical Engineering.

Handbook of Exact Solutions for Ordinary Differential Equations, Second Edition

A. D. Polyanin, A. Polyanin, V. Zaitsev, 2002 .

Various decomposition techniques for linear equations of continuum mechanics

A. Polyanin, S. Lychev, 2014 .

Reaction-Diffusion Models with Delay: Some Properties, Equations, Problems, and Solutions

V. G. Sorokin, A. Polyanin, A. V. Vyazmin, 2018, Theoretical Foundations of Chemical Engineering.

Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction–diffusion equations with variable coefficients

A. Polyanin, 2019, International Journal of Non-Linear Mechanics.

Non-linear blow-up problems for systems of ODEs and PDEs: Non-local transformations, numerical and exact solutions

A. Polyanin, I. Shingareva, 2019, International Journal of Non-Linear Mechanics.

Non-linear problems with non-monotonic blow-up solutions: Non-local transformations, test problems, exact solutions, and numerical integration

A. Polyanin, I. Shingareva, 2017 .

The generating equations method: Constructing exact solutions to delay reaction–diffusion systems and other non-linear coupled delay PDEs

A. Polyanin, A. Zhurov, 2015 .

The functional constraints method: Application to non-linear delay reaction-diffusion equations with varying transfer coefficients

A. Polyanin, A. Zhurov, 2014 .

Ju l 2 01 7 Numerical integration of blow-up problems on the basis of non-local transformations and differential constraints ∗

A. Polyanin, I. Shingareva, 2018 .

Numerical integration blow-up problems on the basis of non-local transformations and differential constraints

A. Polyanin, I. Shingareva, 2017, 1707.03493.

The use of differential and non-local transformations for numerical integration of non-linear blow-up problems

A. Polyanin, I. Shingareva, 2017 .

Functional and generalized separable solutions to unsteady Navier–Stokes equations

A. Polyanin, A. Zhurov, 2016 .

New generalized and functional separable solutions to non-linear delay reaction–diffusion equations

A. Polyanin, A. Zhurov, 2014 .

Non-linear instability and exact solutions to some delay reaction–diffusion systems

A. Polyanin, A. Zhurov, 2014 .

A new method for constructing exact solutions to nonlinear delay partial differential equations

A. Polyanin, A. Zhurov, 2013, 1304.5473.

S I ] 1 9 A pr 2 01 3 A new method for constructing exact solutions to nonlinear delay partial differential equations

A. Polyanin, A. Zhurov, 2013 .

Non-isothermal flows of liquid metals and melts: Qualitative features, asymptotic models, problems, exact and approximate solutions

A. Polyanin, A. Zhurov, 2016 .

Parametrically defined differential equations

A. Polyanin, A. Zhurov, 2017 .

New methods for processing experimental data: Applicability tests for empirical formulas

A. Polyanin, V. V. Dil’man, E. A. Vyaz’mina, 2008 .

Symmetry reductions and new functional separable solutions of nonlinear Klein–Gordon and telegraph type equations

A. Polyanin, A. Zhurov, 2020 .

Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions

A. Polyanin, 2019, Mathematics.

Exact Solutions > Ordinary Differential Equations > Higher-Order Nonlinear Ordinary Differential Equations > Generalized Homogeneous Equation

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Second-Order Nonlinear Ordinary Differential Equations > Second-Order Autonomous Differential Equation

A. Polyanin, Boca Raton, 2004 .

Exact Solutions > Ordinary Differential Equations > First-Order Ordinary Differential Equations > Riccati Equation, Special Case 4

A. Polyanin, 2004 .

If n = -1 and b = 0, we have the Euler equation 2.12. If n ≠ -1 and b ≠ 0, the solution is expressed in terms of Bessel functions:

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Higher-Order Nonlinear Ordinary Differential Equations > Emden-Fowler Equation of the Third-Order

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Higher-Order Nonlinear Ordinary Differential Equations > Equation Does not Depend on y Explicitly

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > First-Order Ordinary Differential Equations > First-Order Homogeneous Differential Equation

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > First-Order Ordinary Differential Equations > Abel Differential Equation of the Second Kind (Special Case)

A. Polyanin, Boca Raton, 2004 .

Second-order constant coefficient linear differential equation. In physics this equation is called an equation of damped vibrations.

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Higher-Order Linear Ordinary Differential Equations > Constant Coefficient Linear Differential Equation

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Second-Order Nonlinear Ordinary Differential Equations > Second-Order Generalized Homogeneous Equation

A. Polyanin, 2004 .

Exact Solutions > Ordinary Differential Equations > Second-Order Linear Ordinary Differential Equations >

A. Polyanin, 2004 .

Multi-Parameter Reaction–Diffusion Systems with Quadratic Nonlinearity and Delays: New Exact Solutions in Elementary Functions

A. Polyanin, A. Zhurov, 2022, Mathematics.

Qualitative analysis of the mass transfer of an ordered system of solid reacting particles at high Peclét numbers

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1979 .

Construction of functional separable solutions in implicit form for non-linear Klein–Gordon type equations with variable coefficients

A. Polyanin, 2019, International Journal of Non-Linear Mechanics.

Partial separation of variables in unsteady problems of mechanics and mathematical physics

A. Polyanin, 2000 .

Structure of solutions to linear unsteady boundary value problems in mechanics and mathematical physics

A. Polyanin, 2000 .

Exact solutions of nonlinear heat- and mass-transfer equations

A. Polyanin, A. Zhurov, A. V. Vyaz’min, 2000 .

Hydrodynamics, Mass and Heat Transfer in Chemical Engineering

Andrei D. Polyanin, A. M. Kutepov, D. A. Kazenin, 2001 .

Nonlinear problems with blow-up solutions: Numerical integration based on differential and nonlocal transformations, and differential constraints

Andrei D. Polyanin, Inna K. Shingareva, A. Polyanin, 2018, Appl. Math. Comput..

Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: Transformations, general solutions, and integration methods

Andrei D. Polyanin, Alexei I. Zhurov, A. Polyanin, 2017, Appl. Math. Lett..

Decomposition methods for coupled 3D equations of applied mathematics and continuum mechanics: Partial survey, classification, new results, and generalizations

A. Polyanin, S. Lychev, Andrei D. Polyanina, 2016 .

Exact Solutions > Algebraic Equations and Systems of Algebraic Equations > Systems of Algebraic Equations > System of Linear Algebraic Equations

A. Polyanin, 2004 .

Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology

A. Polyanin, 2004 .

Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology

A. Polyanin, 2004 .

A method for constructing exact solutions of nonlinear delay PDEs

Andrei D. Polyanin, V. G. Sorokin, Vsevolod G. Sorokin, 2021 .

New exact solutions of nonlinear wave type PDEs with delay

Andrei D. Polyanin, V G Sorokin, V. G. Sorokin, 2020, Appl. Math. Lett..

Exact separable solutions of delay reaction-diffusion equations and other nonlinear partial functional-differential equations

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2014, Commun. Nonlinear Sci. Numer. Simul..

Transformations, properties, and exact solutions of unsteady axisymmetric boundary layer equations for non-Newtonian fluids

A. Polyanin, V. Zaitsev, 2017, Theoretical Foundations of Chemical Engineering.

New classes of exact solutions to nonlinear sets of equations in the theory of filtration and convective mass transfer

A. Polyanin, E. Vyazmina, P. Bedrikovetskii, 2007 .

Functional constraints method for constructing exact solutions to delay reaction-diffusion equations and more complex nonlinear equations

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2014, Commun. Nonlinear Sci. Numer. Simul..

Method of Asymptotic Interpolation in Problems of Chemical Hydrodynamics and Mass Transfer

A. Polyanin, A. V. Vyaz’min, I. Denisov, 2001 .

DECOMPOSITION OF SYSTEMS OF EQUATIONS FOR CONTINUUM MECHANICS 1. ELASTICITY, THERMOELASTICITY, POROELASTICITY

A. Polyanin, Russian Federation., M. State, 2015 .

Functional Separation of Variables in Nonlinear PDEs: General Approach, New Solutions of Diffusion-Type Equations

A. Polyanin, 2020, 2001.01645.

Functional separable solutions of nonlinear reaction-diffusion equations with variable coefficients

Andrei D. Polyanin, A. Polyanin, 2019, Appl. Math. Comput..

The direct method of functional separation of variables can provide more exact solutions than the compatibility analysis of PDEs based on a single differential constraint

A. Polyanin, 2019, 1903.02290.

One-dimensional reductions and functional separable solutions to unsteady plane and axisymmetric boundary-layer equations for non-Newtonian fluids

A. Polyanin, A. Zhurov, 2016 .

Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2016, Commun. Nonlinear Sci. Numer. Simul..

Unsteady axisymmetric boundary-layer equations: Transformations, properties, exact solutions, order reduction and solution method

A. Polyanin, A. Zhurov, 2015 .

Transformations, properties, and exact solutions of nonstationary axisymmetric boundary-layer equations

A. Polyanin, 2015, Theoretical Foundations of Chemical Engineering.

On RF-pairs, Bäcklund transformations and linearization of nonlinear equations

A. Polyanin, A. Zhurov, 2012 .

Transformations and exact solutions of unsteady-state axisymmetric boundary layer equations

A. Polyanin, 2015 .

Exact Solutions of Navier–Stokes, Boundary-Layer, and Heat-Conduction Equations

P. V. Sysoev, A. Polyanin, A. V. Vyaz’min, 2002 .

Methods of Generalized and Functional Separation of Variables in Hydrodynamic and Heat- and Mass-Transfer Equations

A. Polyanin, A. Zhurov, 2002 .

Transformations and exact solutions containing arbitrary functions for boundary-layer equations

A. Polyanin, 2001 .

Partial differential equation

Andrei D. Polyanin, Alexei I. Zhurov, William Schiesser, 2008, Scholarpedia.

Exact solutions to the Navier-Stokes equations with generalized separation of variables

A. Polyanin, 2001 .

Construction of exact solutions to nonlinear PDEs with delay using solutions of simpler PDEs without delay

Andrei D. Polyanin, V. G. Sorokin, Vsevolod G. Sorokin, 2021, Commun. Nonlinear Sci. Numer. Simul..

Decomposition and exact solutions of three-dimensional nonstationary linearized equations for a viscous fluid

A. Polyanin, A. Vyazmin, 2013, Theoretical Foundations of Chemical Engineering.

On order reduction of non-linear equations of mechanics and mathematical physics, new integrable equations and exact solutions

A. Polyanin, A. Zhurov, 2012 .

Von mises- and crocco-type hydrodynamical transformations: Order reduction of nonlinear equations, construction of Bäcklund transformations and of new integrable equations

A. Polyanin, I. Fedotov, 2011 .

New classes of exact solutions and some transformations of the Navier-Stokes equations

A. Polyanin, S. Aristov, 2009, 0909.0446.

Nonlinear instability of the solutions of the Navier-Stokes equations: Formulas for constructing exact solutions

A. Polyanin, 2009 .

Systems of hydrodynamic type equations: Exact solutions, transformations, and nonlinear stability

A. Polyanin, S. Aristov, 2009 .

Equations of hydrodynamic type: exact solutions, reduction of order, transformations, and nonlinear stability/unstability

A. Polyanin, S. Aristov, 2009, 0909.1844.

Exact solutions of unsteady three-dimensional Navier-Stokes equations

A. Polyanin, S. Aristov, 2009 .

The von Mises transformation: order reduction and construction of Backlund transformations and new integrable equations

A. Polyanin, A. Zhurov, 2009, 0907.0586.

New classes of exact solutions to general nonlinear diffusion-kinetic equations

A. Polyanin, E. A. Vyaz’mina, 2006 .

Exact solutions of unsteady boundary layer equations for power-law non-Newtonian fluids

A. Polyanin, 2015 .

Generalized and functional separable solutions to nonlinear delay Klein-Gordon equations

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2014, Commun. Nonlinear Sci. Numer. Simul..

The method of nonlocal transformations: Applications to singularly perturbed boundary-value problems

A. Polyanin, I. Shingareva, 2019, Journal of Physics: Conference Series.

Handbook of Integral Equations

A. Polyanin, 1998 .

Nonlinear Pantograph-Type Diffusion PDEs: Exact Solutions and the Principle of Analogy

Andrei D. Polyanin, V. G. Sorokin, Vsevolod G. Sorokin, 2021, Mathematics.

Exact Solutions and Reductions of Nonlinear Diffusion PDEs of Pantograph Type

V. G. Sorokin, A. Polyanin, 2021, 2103.01666.

Methods for Constructing Complex Solutions of Nonlinear PDEs Using Simpler Solutions

Andrei D. Polyanin, Alexander V. Aksenov, A. Polyanin, 2021, Mathematics.

Construction of complex solutions to nonlinear partial differential equations using simpler solutions

Andrei D. Polyanin, Alexander V. Aksenov, A. Polyanin, 2021, 2102.04815.

Separation of variables in PDEs using nonlinear transformations: Applications to reaction-diffusion type equations

Andrei D. Polyanin, Alexei I. Zhurov, A. Polyanin, 2020, Appl. Math. Lett..

Functional separable solutions of nonlinear convection-diffusion equations with variable coefficients

Andrei D. Polyanin, A. Polyanin, 2019, Commun. Nonlinear Sci. Numer. Simul..

Generalized traveling-wave solutions of nonlinear reaction-diffusion equations with delay and variable coefficients

Andrei D. Polyanin, A. Polyanin, 2019, Appl. Math. Lett..

Nonlinear delay reaction-diffusion equations: Traveling-wave solutions in elementary functions

Andrei D. Polyanin, V. G. Sorokin, Vsevolod G. Sorokin, 2015, Appl. Math. Lett..

New classes of exact solutions to nonlinear systems of reaction-diffusion equations

A. Polyanin, E. A. Vyaz’mina, 2006 .

Review of methods for constructing exact solutions of equations of mathematical physics based on simpler solutions

A. Polyanin, A. Aksenov, 2022, Theoretical and Mathematical Physics.

Nonlinear delay reaction-diffusion equations with varying transfer coefficients: Exact methods and new solutions

Andrei D. Polyanin, Alexei I. Zhurov, A. Polyanin, 2014, Appl. Math. Lett..

Exact solutions of linear and non-linear differential-difference heat and diffusion equations with finite relaxation time

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2013 .

Exact Solutions > Nonlinear Partial Differential Equations > Second-Order Parabolic Partial Differential Equations > FitzHugh-Nagumo Equation

A. Polyanin, 2004 .

A Concise Handbook of Mathematics, Physics, and Engineering Sciences

Andrei D. Polyanin, Alexei Chernoutsan, A. Polyanin, 2010 .

Three-dimensional diffusive boundary-layer problems

A. Polyanin, 1984 .

An approximate method is proposed for the solution of nonlinear boundary problems of convective heat and mass transfer; the method is based on the procedure of "averaging" equations or boundary conditions.

A. Polyanin, V. V. Dil, 1985 .

New methods of the mass and heat transfer theory — II. The methods of asymptotic interpolation and extrapolation

A. Polyanin, V. V. Dil’man, 1985 .

“Averaging” method in problems of convective mass and heat transfer

A. Polyanin, V. V. Dil’man, 1984 .

The change of the diffusivity with the change of the concentration of the solvent in a solution

A. Polyanin, N. Kovatcheva, Z. Zapryanov, 1989 .

Foams as specific gas-liquid technological media

D. A. Kazenin, A. Polyanin, A. V. Vyaz’min, 2000 .

Exact solutions of non-linear differential-difference equations of a viscous fluid with finite relaxation time

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2013 .

Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays

V. G. Sorokin, A. Polyanin, 2023, Mathematics.

Exact solutions of the Navier-Stokes equations with the linear dependence of velocity components on two space variables

A. Polyanin, D. V. Knyazev, S. Aristov, 2009 .

New classes of exact solutions of Euler equations

A. Polyanin, S. Aristov, 2008 .

A new method for constructing exact solutions to three-dimensional Navier-Stokes and Euler equations

A. Polyanin, S. Aristov, 2011 .

Theory of free and forced vibrations of a rigid rod based on the Rayleigh model

A. Polyanin, M. Shatalov, I. Fedotov, 2007 .

New approximate analytic methods of investigating problems of physicochemical mechanics

A. Polyanin, V. V. Dil’man, 1984 .

Method for solution of some non-linear boundary value problems of a non-stationary diffusion-controlled (thermal) boundary layer

A. Polyanin, 1982 .

Convective diffusion to a reacting particle in a fluid. Nonlinear surface reaction kinetics

A. Polyanin, Y. Sergeev, 1980 .

Convective diffusion to a drop under arbitrary conditions of absorption. Diffusion boundary layer approximation

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1980 .

Mass transfer interaction of moving particles in a reactive dispersive system

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1978 .

Mass transfer of particles located on the flow axis at large peclet number

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1977 .

Nonstationary convective heat and mass transfer in a fluid at high peclet numbers

A. Polyanin, P. A. Pryadkin, 1981 .

OF ABSORPTION. DIFFUSION BOUNDARY LAYER APPROXIMATION

A. Polyanin, S. Ryazantsev, 1980 .

Asymptotic solutions of the problem of heat and mass transfer of particles in a fluid

A. Polyanin, 1979 .

Diffusion to a chain of drops (bubbles) at large péclet numbers

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1978 .

Structure of the diffusional wake of an absorbing particle near the critical lines

A. Polyanin, 1977 .

Nonstationary convective heat and mass transfer of droplets for commensurare phase resistances

A. Polyanin, 1984 .

Intensification of mass transfer in a current-carrying fluid at high Péclet numbers

A. Polyanin, P. A. Pryadkin, 1979 .

Diffusional interaction of drops in a liquid

A. Polyanin, 1978 .

Distribution of the concentration in a diffusion wake with stokes flow around a particle

A. Polyanin, 1977 .

Diffusion toward a cylinder in the case of an arbitrary viscous flow. Diffusive boundary layer approximation

A. Polyanin, Yu. N. Syskov, 1976 .

Convective diffusion to a solid particle in the case of nonlinear kinetics of heterogeneous chemical reaction

Yu. P. Gupalo, Yu. S. Ryazantsev, A. Polyanin, 1980 .

New methods of the mass and heat transfer theory—I. The method of asymptotic correction and the method of model equations and analogies

A. Polyanin, V. V. Dtl'man, 1985 .

On nonisothermal chemical reaction at the particle surface in a laminar flow

A. Polyanin, 1982 .

On the nonlinear instability of the solutions of hydrodynamic-type systems

A. Polyanin, 2009 .

A. Polyanin, I. Shingareva, 2022, Publishing Research Quarterly.

Andrei D. Polyanin, Inna K. Shingareva, A. Polyanin, 2021, ArXiv.

Handbook of Linear Partial Differential Equations for Engineers and Scientists, Second Edition

Andrei D. Polyanin, Vladimir E. Nazaikinskii, A. Polyanin, 2016 .

Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay

V. G. Sorokin, A. Polyanin, 2023, Mathematics.

Hypersingular nonlinear boundary-value problems with a small parameter

Andrei D. Polyanin, Inna K. Shingareva, A. Polyanin, 2018, Appl. Math. Lett..

Analysis for an N-stepped Rayleigh bar with sections of complex geometry

A. Polyanin, M. Shatalov, I. Fedotov, 2008 .

Longitudinal vibrations of a Rayleigh-Bishop rod

I. A. Fedotov, A. Polyanin, M. Shatalov, 2010 .

On One Method for Constructing Exact Solutions of Nonlinear Equations of Mathematical Physics

A. Polyanin, A. Zhurov, 2019, Doklady. Mathematics.

Handbook of Exact Solutions for Ordinary Differential Equations

A. Polyanin, V. Zaitsev, A. D. Poli︠a︡nin, 1995 .

Integration of linear and some model non-linear equations of motion of incompressible fluids

A. Polyanin, A. Zhurov, 2013 .

Partial differential equation

A. Polyanin, W. Schiesser, A. Zhurov, 2008, Scholarpedia.

Handbook of Nonlinear Partial Differential Equations, Second Edition

A. Polyanin, V. Zaitsev, 2011 .

Mass transfer from a particle in a shear flow with surface reactions

A. Polyanin, N. Kovatcheva, V. N. Kurdjumov, 1993 .

Separation of Variables and Exact Solutions to Nonlinear PDEs

A. Polyanin, A. Zhurov, 2021 .

Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems

Andrei D. Polyanin, Valentin Zaitsev, A. Polyanin, 2017 .

A. D. Polyanin, I. K. Shingareva, A. Polyanin, 2021, ArXiv.

Exact solutions to homogeneous and quasi-homogeneous systems of nonlinear ODEs

Alexei I. Zhurov, Andrei D. Polyanin, A. Polyanin, 2021, 2107.10759.

Comparison of the Effectiveness of Different Methods for Constructing Exact Solutions to Nonlinear PDEs. Generalizations and New Solutions

A. Polyanin, 2019, Mathematics.

The method of non-local transformations: Applications to blow-up problems

A. Polyanin, I. Shingareva, 2017 .

Exact solutions to differential-difference heat and mass transfer equations with a finite relaxation time

A. Polyanin, 2014, Theoretical Foundations of Chemical Engineering.

Upscaling of the Waterflood Reservoir Properties on the Core Level: Laboratory Study, Macro and Micro Modelling

P. G. Bedrikovetsky, K. T. Potsch, A. D. Polyanin, 1995 .