... Explicit Solutions of Nonlinear Heat Equations . ... It was recently proposed a new method for finding differential constraints which uses linear determining equations. ... In this report we start with determination of the solutions of linear determining equations of the second and third orders for the nonlinear diffusion equation. ... At last we derive exact solutions of some two-dimension equation. Bibliography   O.V.Kaptsov (1998) Linear determining equations for differential constraints. ...

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• AUTHOR : Verevkin I
• Modern Group Analysis (MOGRAN 9)

... 4) Percolation probability: [pic] , where L is linear size of lattice. ... The presence of obstacles in a system leads to: - increase of the critical concentration value; this effect grows with increase of the full area of obstacles and falls with increase of the linear size of ones. - increase of the critical exponent ( value; this effect increase with growth both of linear size of obstacles and of their full area. - increase of the growth rate of ...

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... Basic statement: "Mathematics is much clever, than Mathematician" It means, that after the scientist or engineer developed new mathematical model and designed corresponding equations, the solution to these equations produces new information unpredictable for the author! ... This vibration excites the shear wave in tissue 2 sx 2 - (ct + ) s x = Fx 2 t t Studies in Fluid Dynamics of water jet are connected with two main problems: 1. Flows in contracting nozzle forming high-speed jet. ...

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