相关论文: An analytical solution of the weighted Fermat-Torr…
On polytopal domains in $\mathbb{R}^3$, we prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian with analytic right-hand side. Employing the Caffarelli-Silvestre extension allows to…
In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…
We determine a positive real number (weight), which corresponds to a vertex of a tetrahedron and it depends on the three weights which correspond to the other three vertices and an infinitesimal number $\epsilon.$ As a limiting case, for…
We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary…
Relative equilibria on a rotating meridian on $\mathbb{S}^2$ in equal-mass three-body problem under the cotangent potential are determined. We show the existence of scalene and isosceles relative equilibria. Almost all isosceles triangles,…
We present explicit analytical solution for the problem of minimization of the function $ F(x,y)= \sum_{j=1}^3 m_j \sqrt{(x-x_j)^2+(y-y_j)^2} $, i.e. we find the coordinates of stationary point and the corresponding critical value of $…
In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat's problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric…
In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new…
We provide the general solution of problems concerning AC star circuits by turning them into geometric problems. We show that one problem is strongly related to the Fermat-point of a triangle. We present a solution that is well adapted to…
We develop a multidensity formulation of the Ornstein-Zernike equation with Percus-Yevick closure for hard spheres with anisotropic surface adhesion of tetrahedral quadrupolar-like symmetry. An analytical solution is obtained using the…
This article focuses on the occurrence of 3-point configurations in subsets of $\mathbb{R}^d$ of sufficient thickness. We prove that a compact set $A\subset \mathbb{R}^d$ contains a similar copy of any linear $3$-point configuration (such…
The Florides solution, proposed as an alternative to the interior Schwarzschild solution, represents a static and spherically symmetric geometry with vanishing radial stresses. It is regular at the center, and is matched to an exterior…
Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a…
The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to…
We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4…
We show that there is no $(1+\eps)$-approximation algorithm for the problem of covering points in the plane by minimum number of fat triangles of similar size (with the minimum angle of the triangles being close to 45 degrees). Here, the…
In the $2$-dimensional $n$-body problem, $n\ge 3$, in spaces of constant curvature, $\kappa\ne 0$, we study polygonal homographic solutions. We first provide necessary and sufficient conditions for the existence of these orbits and then…
Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertices of the outer face to the vertices of a convex polygon, and…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…
We generalize the Fenchel theorem for strong spacelike closed curves of index $1$ in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to $2\pi$. Here strong spacelike means that the tangent…