Related papers: The Baumkuchen Theorem
The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in…
This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.
We give a geometric approach to the proof of the $\lambda$-lemma. In particular, we point out the role pseudoconvexity plays in the proof.
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a…
The deleting items and disturbing mesh theorems of Riemann Integral are extended to multiple integral,line integral and surface integral respectively by constructing various of incomplete Riemann sum and non-Riemann sum sequences which…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
We give here a general, best-possible, and smoothly-derived form of the Master Theorem for divide-and-conquer recurrences.
Mishchenko's theorem states that piecewise smooth and Lie algebroid cohomology of a transitive Lie algebroid defined over a combinatorial manifold are isomorphic. In this paper, we describe two applications of that result. The first…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
We explain how the theory of sandwich cellular algebras can be seen as a version of cell theory for algebras. We apply this theory to many examples such as Hecke algebras, and various monoid and diagram algebras.
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…
For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher…
We introduce the notion of a chopped and sliced cone in combinatorial geometry and prove two structure theorems for the number of integral points in the individual slices of such a cone. We observe that this notion applies to weight…
We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence…
A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.
Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
In the present popular science paper we determine when a square can be dissected into rectangles similar to a given rectangle. The approach to the question is based on a physical interpretation using electrical networks. Only secondary…