Transformations $z(t)=L(t)y(\varphi (t))$ of ordinary differential equations

Václav Tryhuk

Displaying similar documents to “Transformations $z (t) = L (t) y (ϕ (t))$ of ordinary differential equations”

On transformations $z (t) = y (ϕ (t))$ 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 the order $n + 1$ $(n \geq 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form $f (s, v, w_{11} v_{1}, ..., \sum_{j = 1}^{n} w_{n j} v_{j}) = \sum_{j = 1}^{n} w_{n + 1 j} v_{j} + w_{n + 1 n + 1} f (x, v, v_{1}, ..., v_{n}),$ where $w_{i j} = a_{i j} (x_{1}, ..., x_{i - j + 1})$ are given functions, $w_{n + 11} = g (x, x_{1}, ..., x_{n})$ , is solved on $ℝ .$

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 $T^{A} T * \to T * T^{A}$ depending on a linear function defined on the Weil algebra A. We show that for many particular cases of A, all natural transformations $T^{A} T * \to T * T^{A}$ 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, ,...

Convergence acceleration of shifted $L R$ transformations for totally nonnegative Hessenberg matrices

Akiko Fukuda, Yusaku Yamamoto, Masashi Iwasaki, Emiko Ishiwata, Yoshimasa Nakamura (2020)

Applications of Mathematics

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We design shifted $L R$ transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted $L R$ transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted $L R$ transformations by considering the concept of the Newton...

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 $y \neq 0$ , $v \neq 0 .$

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

On transformations z ( t ) = y ( ϕ ( t ) ) of ordinary differential equations

Natural transformations of the composition of Weil and cotangent functors

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

Convergence acceleration of shifted L R transformations for totally nonnegative Hessenberg matrices

On global transformations of ordinary differential equations of the second order

Displaying similar documents to “Transformations $z (t) = L (t) y (ϕ (t))$ of ordinary differential equations”

On transformations $z (t) = y (ϕ (t))$ of ordinary differential equations

Convergence acceleration of shifted $L R$ transformations for totally nonnegative Hessenberg matrices