Related papers: Solution of the Ovals problem

We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.

We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.

This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…

We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.

In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.

A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.

We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of C. Bender and E. Ben-Naim. We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel…

We derive solvability conditions and closed-form solution for the Weber type integral equation, related to the familiar Weber-Orr integral transforms and the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22 (2) (1924),…

The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.

Some solutions of the Heavenly equations and their generalizations are considered

We provide algorithms for the absolute and alternating Ostrowski Expansions of the continuum and provide proofs for their uniqueness.

We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…

In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with a nonlinear deterministic clock.

An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal,…

In this paper, we provide a systematic way of finding explicit solutions for a class of continuous fragmentation equations with growth or decay in the state space and derive explicit solutions in the cases of constant and linear…

The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special…

We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…

Using the Operator Product Expansion for Wilson loops we derive a simple formula giving the discontinuities of the two loop result in terms of the one loop answer. We also argue that the knowledge of these discontinuities should be enough…

We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in $\bC^n$. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian…

An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.