Related papers: X- problem of value three
In this paper some Hadamard-type inequalities for convex functions of 3-variables on a rectanguler box are given. We also define a mapping related to convex functions on a rectanguler box.
We provide infinitely many solutions of a Dirichlet problem on balls.
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
The article studies a generalization of the classical Fermat-Torricelli problem to normed spaces of arbitrary finite dimension. Necessary and sufficient conditions for the uniqueness of the solution of the Fermat-Torricelli problem for any…
An observation on Hall-Littlewood polynomials.
We present a deterministic polynomial-time algorithm that solves the 3-satisfiability problem.
In this paper we investigate the series $\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n}x^k$. Obtaining some integral representations of them, we evaluated the sum of them explicitly for $n = 0, 1, 2$.
Some inequalities for different types of convexity are established.
The time-periodic problem on the Boltzmann equation with a given time-periodic external force in the three-dimensional whole space has remained open since it was first studied in [15] for only spatial dimensions not less than five. The goal…
We study a noncommutative version of the Zariski cancellation problem for some classes of connected graded Artin-Schelter regular algebras of global dimension three.
In this paper we present the algorithm of finding the solutions of the equation $x^3+ax=b$ in $\mathbb{Z}^*_3$ with coefficients from $\mathbb{Q}_3$.
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
The paper is concerned with Lax representations for the three-dimensional Euler--Helmholtz equation. We show that the parameter in the Lax representation from Theorem 3 in [15] is non-removable. Then we present two new Lax representations…
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…
We discuss the computational complexity of special cases of the 3-dimensional (axial) assignment problem where the elements are points in a Cartesian space and where the cost coefficients are the perimeters of the corresponding triangles…
In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
The normality equations for the Newtonian dynamical systems on an arbitrary Riemannian manifold of the dimension $n \geq 3$ are considered. Locally the solution of such equations reduces to three possible cases: in two of them the solution…
We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.