We describe a set of algorithms (and corresponding codes) that serve as a basis for an automated proof of existence of a certain dynamical behaviour in a given dynamical system. In particular it is in principle possible to automatically verify the presence of complicated dynamics using these tools. The Hénon map is used to illustrate these techniques.

In 1970, E. M. Andreev published a classification of all three dimensional compact hyperbolic polyhedra having non-obtuse dihedral angles [3]. Given a combinatorial description of a polyhedron, C, Andreev’s Theorem provides five classes of linear inequalities, depending on C, for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron real...

the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

This paper investigates the existence and uniqueness of solutions to rst-order nonlinear boundary value problems (BVPs) involving fuzzy dif- ferential equations and two-point boundary conditions. Some sucient condi- tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.

the existence is a categorical concept according to kant’s philosophy. kant, going to be a subjectivist philosopher, negates the existence as a perfection and concludes the separation between the mind and extra-mental world. but the externality is not an origin which we deny it easily, even if it is faced with multiple problems such as the issue of simplicity and multiplicity and also being his...

sleep problems are common complaints among pregnant women. this study was designed to compare subjective sleep problems in non-pregnancy condition, healthy and preeclamptic pregnancy as a major complication of pregnancy. we hypothesized that some sleep problems are more prevalent in females with preeclampsia.in this cross-sectional study, 102 women with preeclampsia, 106 healthy pregnant women ...