Related papers: On Generalizations of the Butterfly Theorem

Pappus' Involution Theorem is a powerful tool for proving theorems about non-euclidean triangles and generalized triangles in Cayley-Klein models. Its power is illustrated by proving with it some theorems about euclidean and non-euclidean…

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and…

We give a sheaf-theoretic version of the universal coefficient theorem.

In the past hundred years, chaos has always been a mystery to human beings, including the butterfly effect discovered in 1963 and the dissipative structure theory which won the chemistry Nobel Prize in 1977. So far, there is no quantitative…

We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring invariant in that case. The polynomial is an invariant of a…

We give a projective proof of the butterfly porism for cyclic quadrilaterals and present a general reversion porism for polygons with an arbitrary number of vertices on a conic. We also investigate projective properties of the porisms.

The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…

In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…

Algebraic deformations of modules over a ring are considered. The resulting theory closely resembles Gerstenhaber's deformation theory of associative algebras.

A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an…

In this note we present variants of Kostov's theorem on a versal deformation of a parabolic point of a complex analytic $1$-dimensional vector field. First we provide a self-contained proof of Kostov's theorem, together with a proof that…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…

Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and…

We prove in a very general framework several versions of the classical Poincar\'e-Birkhoff-Witt Theorem, which extend results from [BeGi, BrGa, CS, HvOZ, WW]. Applications and examples are discussed in the last part of the paper.

This paper extends de Rham theory of smooth manifolds to exploded manifolds. Included are versions of Stokes' theorem, De Rham cohomology, Poincare duality, and integration along the fiber. The resulting cohomology theory is used to define…

The aim of this paper is to present an extension theorem for the functions separately holomorphic on generalized (N,k)-crosses with pluripolar singularities.