Related papers: Solution of the Ovals problem
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 paper we present a two-component generalization of the C-integrable Calogero equation (see [1]). This system is C-integrable as well, and moreover we show that the Calogero equation and its two-component generalization are solvable…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.
In this paper we prove the decidability of the HD0L ultimate periodicity problem.
A generalization of the law of total covariance is presented and proved.
We present a new recursion and Hamiltonian operators for the Viallet equation. This new recursion operator and the recursion operator found in [Theoretical and Mathematical Physics, 167:421--443 (2011), arXiv:1004.5346] satisfy the elliptic…
In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan and the author constructed spatially periodic solutions, whereas in this paper the…
In this article uncoditional solvability of the Carleman-Vekua equation with a singular point is proved, the Riemann-Hilbert problem is solved integral representations of solutions, the strictures of their zeros and poles are recieved.
We introduce new classes of solutions to the three dimensional Navier-Stokes equations in the whole and half spaces that add rotational correction to self-similar and discretely self-similar solutions. We construct forward solutions in…
In this paper the benefits of affine quantization method are highlighted through oscillation problems. We show how affine quantization is able to solve oscillation problems where canonical quantization fails.
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
In this paper, using the technical tools in \cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the K\"ahler case results in \cite{HMW} and \cite{DK}.
In this paper we study the the Gauss image problem, which is a generalization of the Aleksandrov problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we…
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on…
We show, that under natural assumptions, solutions of Dirichlet problems for uniformly elliptic divergence form operator can be approximated pointwise by solutions of some versions of Robin problems. The proof is based on stochastic…
In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…