Related papers: Solution of the Ovals problem

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)…

This paper gives out the solution of divergent Navier-Stokes equations, and shows that in this case, under a physicalacceptable condition, the solution would be smooth .

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \begin{equation*}\left\{ \begin{array}{cc}-\func{div}\left( \omega _{1}(x)\left\vert \nabla u\right\vert^{p(x)-2}\nabla…

In this note we extend a theorem from [13] about uniform circle random coverings

We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

A formulation of the Maxwell equations in terms of the split octonions is presented.

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one…

In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…

In this paper we obtain a new parametric solution of the problem of finding two triads of biquadrates with equal sums and equal products.

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…

We propose a new approach to solve an NP complete problem by means of stochastic limit.

In this paper we obtain an algorithm towards solving the two-dimensional moment problem. This algorithm gives the necessary and sufficient conditions for the solvability of the moment problem. It is shown that all solutions of the moment…

In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.

In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1x_1+a_2x_2+...+a_sx_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and…

We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed…

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

The solution of one Zamfiresku's problem was obtained. We discuss the unsolved questions related to the Mizel's problem.