相关论文: Miquel circles and Cevian lines

We inquire into the relation between the curl operators, the Poisson coboundary operators and contravariant derivatives on Poisson manifolds to study the theory of differential operators in Poisson geometry. Given an oriented Poisson…

We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be…

The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G. For any simple G, there exist compact manifolds with the same classical equivariant…

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.

We define and examine flip operations for quadrilateral and hexahedral meshes, similar to the flipping transformations previously used in triangular and tetrahedral mesh generation.

The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are…

We provide a companion to the recent Benyi-Curgus generalization of the well-known theorems of Ceva and Menelaus, so as to characterize both the collinearity of points and the concurrence of lines determined by six points on the edges of a…

The theorem on the existence of bifurcation points of the stationary solutions for the Vlasov-Maxwell system with bifurcation direction is proved.

Here is presented a concept of centrogeometry which can be seen as a combination of the concept of point-like observer with an idea of Poincar\'{e}'s that different geometries are principally equivalent. As it is to be shown later, all…

We introduce the notion of operadic torsors and operadic quasi-torsors. We show that if an operadic (quasi-)torsor between two operads exists, then these operads are (quasi-)isomorphic. As an application we present the (arguably) shortest…

Characterizations of binary operations between convex bodies on the Euclidean unit sphere are established. The main result shows that the convex hull is essentially the only non-trivial projection covariant operation between pairs of convex…

The theory of deformed plates in mechanical equilibrium is formulated and properties of circular plates lifted at the center are discussed.

The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of…

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…

A triangulation of a polygon is a subdivision of it into triangles, using diagonals between its vertices. Two different triangulations of a polygon can be related by a sequence of flips: a flip replaces a diagonal by the unique other…

We characterize all natural linear operations between spaces of differential forms on contact manifolds. Our main theorem says roughly that such operations are built from some algebraic operators which we introduce and the exterior…

We consider the configuration space of ordered points on the two-dimensional sphere that satisfy a specific system of quadratic equations. We construct periodic orbits in this configuration space using elliptic theta functions and show that…

Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…

The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…