Related papers: "`Painleve 34"' equation: equivalence test

In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.

Starting from the second Painlev\'{e} equation, we obtain Painlev\'{e} type equations of higher order by using the singular point analysis.

A Riemann-Hilbert problem for a $q$-difference Painlev\'e equation, known as $q\textrm{P}_{\textrm{IV}}$, is shown to be solvable. This yields a bijective correspondence between the transcendental solutions of $q\textrm{P}_{\textrm{IV}}$…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

In this note we resolve the problem of getting a state-space realization compatible with the deterministic state-space realization and the filtering problem.

We offer elementary proofs for fundamental properties of solutions to the homogeneous second Painlev\'e equation.

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the exampes the…

The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…

We prove the Complete nontrivial cycle-intersection theorem for systems of permutations.

Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.

Exact single-wave and two-wave solutions of systems of equations of Newell-Whitehead type are presented. The Painleve test and calculations in the spirit of Hirota are used to construct these solutions.

We shall study the equivalence problem for ordinary differential equations with respect to the affine transformations group.

We claim to resolve the P=?NP problem via a formal argument for P=NP.

Problem of asymptotic description for global solutions to the six Painleve equations was investigated. Elliptic anzatzes and appropriate modulation equations were written out.

In this paper we give necessary and sufficient conditions for the equality case in Wielandt's eigenvalue inequality.

We produce arbitrarily large equivalence classes of matings with the aeroplane polynomial. These are obtained by a slight generalisation of the technique of proof of a similar result for Wittner captures.

We utilise a recent approach via the so-called re-scaling method to derive a unified and comprehensive theory of the solutions to Painleve's differential equations (I), (II) and (IV), with emphasis on the most elaborate equation (IV).

Equivalencies of many basic elementary inequalities are given

We provide infinitely many solutions of a Dirichlet problem on balls.