Related papers: Miquel circles and Cevian lines
In this paper we obtain cyclic pentagons and hexagons with rational sides, diagonals and area all of which are expressed in terms of rational functions of several arbitrary rational parameters. On suitable scaling, we obtain cyclic…
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval,…
We identify the maximal chiral algebra of conformal cyclic orbifolds. In terms of this extended algebra, the orbifold is a rational and diagonal conformal field theory, provided the mother theory itself is also rational and diagonal. The…
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…
This paper establishes three minimax theorems for possibly nonconvex functions on Euclidean spaces or on infinite-dimensional Hilbert spaces. The theorems also guarantee the existence of saddle points. As a by-product, a complete solution…
A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area.…
New fundamental mathematical structures are introduced by the triples (left semistructure,right semistructure,bisemistructure) associated with the classical mathematical structures and such that the bisemistructures,resulting from the…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
We give a new proof of the formula expressing the area of the triangle whose vertices are the projections of an arbitrary point in the plane onto the sides of a given triangle, in terms of the geometry of the given triangle and the location…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
An elementary geometric construction known as Napoleon's theorem produces an equilateral triangle built on the sides of any initial triangle: the centroids of each equilateral triangle meeting the original sides, all outward or all inward,…
We introduce an invariant of umbilic points on surfaces in the Euclidean or Minkowski 3-space that counts the maximum number of stable umbilic points they can split up under deformations of the surfaces. We call that number the multiplicity…
In this short note we review some facts about elliptic differential operators on Riemannian manifolds.
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…
In this article we present a detailed study of the existing constructions of colilimits in the category of symmetrical operations. In addition, some examples of operads obtained from colimits of other operads are presented.