Related papers: Simple proofing of Jordan's theorem
This paper presents some results on simple exceptional Jordan algebra over algebraically closed field $\Phi$ with characteristic not 2. Namely an example of simple decomposition of $H(O_3)$ into the sum of two subalgebras of the type…
Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
A proof of the uniformization theorem of Riemann surface is given with only elementary properties of holomorphic functions and not using the paracompacity of the surface. This proof leans on an holomorphic version of the topological…
We study compact stable embedded minimal surfaces whose boundary is given by two collections of closed smooth Jordan curves in close planes of Euclidean 3-space. Our main result is a classification of these minimal surfaces, under certain…
We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnected.
Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…
We give a simple proof of the well-known divisibility by 2 condition for rational points on elliptic curves with rational 2-torsion. As an application of the explicit division by $2^n$ formulas obtained in Sec.2, we construct versal…
Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
In this paper, we investigate the problem of separating a set $X$ of points in $\mathbb{R}^{2}$ with an arrangement of $K$ lines such that each cell contains an asymptotically equal number of points (up to a constant ratio). We consider a…
In this paper we determine all types and the canonical forms of simple subalgebras for each type of simple Jordan algebras and the number of conjugate classes corresponding to the given simple Jordan algebra.
This paper proves a number of flatness results for centralizers of sections of a reductive group scheme over a general base scheme. To this end, we establish relative versions of the Jordan decomposition. Using our results, we obtain a…
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.
We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.
We consider the issue of when the L-polynomial of one curve over $\F_q$ divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a hypothesis that two curves have the same number of points…
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.