Related papers: "`Painleve 34"' equation: equivalence test
In this paper some open problems for Painlev\'e equations are discussed. In particular the following open problems are described: (i) the Painlev\'e equivalence problem; (ii) notation for solutions of the Painlev\'e equations; (iii)…
We prove that the quiver problem is NP complete.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
An interpolation problem related to the elliptic Painlev\'e equation is formulated and solved. A simple form of the elliptic Painlev\'e equation and the Lax pair are obtained. Explicit determinant formulae of special solutions are also…
This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…
In this paper we propose an efficient solution of an equivalence problem for semisimple cyclic codes.
Polynomials related to rational solutions of Painleve' equations satisfy certain difference equations. Conditions are given to acertain that all solutions really are polynomials.
For an arbitrary ordinary second order differential equation a test is constructed that checks if this equation is equivalent to Painleve I, II or Painleve III with three zero parameters equations under the substitutions of variables. If it…
In this paper, we prove that the Fechner and Stevens laws are equivalent (coincide up to isomorphism). Therefore, the problem does not exist.
It is demonstrated that a certain integral equation can be solved using the Painleve equation of third kind. Inversely, a special solution of this Painleve equation can be expressed as the ratio of two infinite series of spheroidal…
A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We consider connection between the Painleve-6 equation and explicitly uniformizable orbifolds
The title says it all.
We show two results of mean value problem, Smale's mean value problem is comprehensively solved in this paper.
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We offer elementary proofs for fundamental properties of the unique triple-zero solution to the first Painlev\'e equation.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
A polynomial algorithm is obtained for the NP-complete linear ordering problem.