相关论文: Simple proofing of Jordan's theorem

We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.

We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.

In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of…

Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra…

We consider collections of disjoint simple closed curves in a compact orientable surface which decompose the surface into pairs of pants. The isotopy classes of such curve systems form the vertices of a 2-complex, whose edges correspond to…

In this paper, we present a short proof of Halin's grid theorem.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

The aim of this paper is to present a very simple original, purely formal, proof of Quillen's adjunction theorem for derived functors, and of some more recent variations and generalizations of this theorem. This is obtained by proving an…

We compute and provide a detailed description on the Jordan constants of the multiplicative subgroup of quaternion algebras over number fields of small degree. As an application, we determine the Jordan constants of the multiplicative…

We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

For two disjoint rectifiable star-shaped Jordan curves (including round circles) in the asymptotic boundary of hyperbolic 3-space, if the distance (see Definition 1.8) between these two Jordan curves are bounded from above by some constant,…

In this paper we prove a relative version of the classical Mumford-Newstead theorem for a family of smooth curves degenerating to a reducible curve with a simple node. We also prove a Torelli-type theorem by showing that certain moduli…

We provide a simple proof of the existence of a planar separator by showing that it is an easy consequence of the circle packing theorem. We also reprove other results on separators, including: (A) There is a simple cycle separator if the…

We prove that any disjoint union of finitely many simple curves in the upper half-plane can be generated in a unique way by the chordal multiple-slit Loewner equation with constant weights.

While planar graphs are flat from a topological viewpoint, we observe that they are not from a geometric one. We prove that every planar graph can be embedded into a surface consisting of spheres, glued together in a tree-like fashion. As a…

This note presents a simple proof of the characteristic function of Student's $t$-distribution. The method of proof, which involves finding a differential equation satisfied by the characteristic function, is applicable to many other…

We give a solution of Plateau's problem for singular curves possibly having self-intersections. The proof is based on the solution of Plateau's problem for Jordan curves in very general metric spaces by Alexander Lytchak and Stefan Wenger…