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 ℝ , u ≠ 0 .

On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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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 ℝ 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.

Digital shapes, digital boundaries and rigid transformations: A topological discussion

Yukiko Kenmochi, Phuc Ngo, Nicolas Passat, Hugues Talbot (2013)

Actes des rencontres du CIRM

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Curvature is a continuous and infinitesimal notion. These properties induce geometrical difficulties in digital frameworks, and the following question is naturally asked: “How to define and compute curvatures of digital shapes?” In fact, not only geometrical but also topological difficulties are also induced in digital frameworks. The – deeper – question thus arises: “Can we still define and compute curvatures?” This latter question, that is relevant in the context of digitization, ,...

Natural transformations of semi-holonomic 3-jets

Gabriela Vosmanská (1995)

Archivum Mathematicum

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Let J ¯ 3 be the functor of semi-holonomic 3 -jets and J ¯ 3 , 2 be the functor of those semi-holonomic 3 -jets, which are holonomic in the second order. We deduce that the only natural transformations J ¯ 3 → J ¯ 3 are the identity and the contraction. Then we determine explicitely all natural transformations J ¯ 3 , 2 → J ¯ 3 , 2 , which form two 5 -parameter families.