Related papers: The generalization of Miquels theorem
Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.
We introduce a theory of Clifford semialgebra systems, with application to representation theory via Hasse-Schmidt derivations on exterior semialgebras. Our main result, after the construction of the Clifford semialgebra, is a formula…
In this paper we first offer an alternative approach to extend the original Fueter's Theorem in Dunkl-Clifford analysis to a version of the higher order case. Then this result is used to prove a generlized version of Fueter's Theorem with…
We derive a set of Clifford-algebraic formulas for two major nonlinear conformal transformations of the physical quantities related to Maxwell's equations. The superiority of these formulas over their vector-tensorial counterparts are…
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
Two theorems are presented concerning the Miquel point configuration, when the operative points on the sides of the triangle are the feet of Cevians,
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
In this article, written primarily for physicists and geometers, we survey several manifestations of a general localization principle for orbifold theories such as $K$-theory, index theory, motivic integration and elliptic genera.
Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on…
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We generalize the Oka extension theorem, and obtain bounds on the norm of the extension, by using operator theory.
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
In this article we consider generalisation of Michelson contrast for positive operators of countably decomposable $W^*$-algebras and find a few several of its properties.
We give two generalizations of Kac's Theorem on representations of quivers. One is to representations of equipped graphs by relations, in the sense of Gelfand and Ponomarev. The other is to representations of quivers in which certain of the…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
This article proves a Pythagoras-type formula for the sides and diagonals of a polygon inscribed in a semicircle having one of the sides of the polygon as diameter.
Our goal is to generalize the Choe-Hoppe helicoid and Clifford cones in Euclidean space. By sweeping out $L$ indpendent Clifford cones in ${\mathbb{R}}^{2N+2}$ via the multi-screw motion, we construct minimal submanifolds in…
A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…