Related papers: Formulas generalizing Pappus and Desargues
A generalized three-form field is an extended version of the canonical three-form field by considering a Lagrangian of the generalized three-form field as a function of the kinetic and the mass terms. In this work, we investigated…
We prove some analogues of the central point theorem and Tverberg's theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.
Three generalizations of the well-known Ceva's Theorem are given in this paper and some applications.
We provide two independent systematic methods of performing $D$-dimensional physical-state sums in gauge theory and gravity in such a way so that spurious light-cone singularities are not introduced. A natural application is to generalized…
We present a description of two dimensional Yang-Mills gauge theory on the plane and on compact surfaces, examining the topological, geometric and probabilistic aspects.
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
We give an abstract framework to transfer generalized amalgamation from a simple theory to another, and we apply it to theories of lovely pairs and of bounded PAC structures. We show in particular that bounded pseudo-algebraically closed…
We prove the (generalized) coherence conjecture of Pappas and Rapoport. As a corollary, one theorem of Pappas an Rapoport, which describes the geometry of the special fibers of the local models for ramified unitary groups, holds…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
The gauge theoretical formulation of general relativity is presented. We are only concerned with local intrinsic geometry, i.e. our space-time is an open subset of a four-dimensional real vector space. Then the gauge group is the set of…
In the paper it is considered the generalized Faber polynomials defined inside and outside a regular curve on the complex plane. The weighted Smirnov spaces corresponding to bounded and unbounded regions are defined. It is proved that the…
A point $P$ in projective space is said to be Galois with respect to a hypersurface if the function field extension induced by the projection from $P$ is Galois. We present a hyperplane section theorem for Galois points. Precisely, if $P$…
In this note, by the umbra calculus method, the Sun and Zagier's congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also provided.
A relativistic generalization of the rational Calogero model is obtained by using the deformation of a gauging matrix system with extra semi-dynamical variables. The Hamiltonian of this system is derived by imposing the gauge fixing…
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Regular generalizations of spherically and axially symmetric metrics and their properties are considered. Newton gravity law generalizations are reduced for null geodesic.