Displaying similar documents to “On the compressed Descartes-plane and its applications.”

Connectivity of diagonal products of Baire one functions

Aleksander Maliszewski (1994)

Fundamenta Mathematicae

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We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.

Three two-dimensional Weyl steps in the circle problem I. The Hessian determinant

Ulrike M. A. Vorhauer, Eduard Wirsing (1999)

Acta Arithmetica

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1. Summary. In a sequence of three papers we study the circle problem and its generalization involving the logarithmic mean. Most of the deeper results in this area depend on estimates of exponential sums. For the circle problem itself Chen has carried out such estimates using three two-dimensional Weyl steps with complicated techniques. We make the same Weyl steps but our approach is simpler and clearer. Crucial is a good understanding of the Hessian determinant that appears...

Qualitative investigation of nonlinear differential equations describing infiltration of water

Xingbao Wu (1995)

Annales Polonici Mathematici

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A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.