Related papers: Solution of the Ovals problem
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
We present for the first time an explicit, complete and closed-form solution to the three-dimensional problem of two fixed centres, based on Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our…
This paper will be replaced later by a revised version.
A proposed solution to the Riemann Hypothesis
In this paper, on envelopes created by circle families in the plane, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.
We give description of rational solutions of polynomial-equations.
In this paper, we obtain the existence result of smooth solutions to the Orlicz-Aleksandrov problem from the perspective of geometric flow. Furthermore, a special uniqueness result of solutions to this problem shall be discussed.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
The solution of Apollonius' problem on constructing a circle (line), tangent to three given circles (lines), is presented in terms of oriented circles and inversive invariants. Tangency is understood as the coincidence of tangent vectors at…
Completely solved the equivalence problem for the "`Painleve 34"' equation.
Integral representation for harmonic function in the ring is constructed in this work. We prove the existence and uniqueness of solutions of the Cauchy problem for the Laplace equation in the ring. Integral representation for the solution…
Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
The aim of this paper is to generalize Apollonius' problem. The problem is to construct a circle that is tangent to three given circles in a plane. We find the maximum possible number of solution circles in the case of more than the three…
Suppose that m is a positive integer, not a perfect square. We present a formula solution to the 2-variable Frobenius problem in Z[\sqrt m] of the "first kind" ([3]).