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Displaying similar documents to “On transformations z ( t ) = y ( ϕ ( t ) ) of ordinary differential equations”

Transformations z ( t ) = L ( t ) y ( ϕ ( t ) ) of ordinary differential equations

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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The paper describes the general form of an ordinary differential equation of an order n + 1 ( n 1 ) which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form f s , w 00 v 0 , ... , j = 0 n w n j v j = j = 0 n w n + 1 j v j + w n + 1 n + 1 f ( x , v , v 1 , ... , v n ) , where w n + 1 0 = h ( s , x , x 1 , u , u 1 , ... , u n ) , w n + 1 1 = g ( s , x , x 1 , ... , x n , u , u 1 , ... , u n ) and w i j = a i j ( x 1 , ... , x i - j + 1 , u , u 1 , ... , u i - j ) for the given functions a i j is solved on , u 0 .

On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

Similarity:

The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form f ( t , v y , w y + u v z ) = f ( x , y , z ) u 2 v + g ( t , x , u , v , w ) v z + h ( t , x , u , v , w ) y + 2 u w z is solved on for y 0 , v 0 .

Natural transformations of the composition of Weil and cotangent functors

Miroslav Doupovec (2001)

Annales Polonici Mathematici

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We study geometrical properties of natural transformations T A T * T * T A depending on a linear function defined on the Weil algebra A. We show that for many particular cases of A, all natural transformations T A T * T * T A can be described in a uniform way by means of a simple geometrical construction.