相关论文: La Derivada del Coseno
Let $f$ be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove new covering results, we extend their theorem to prove the…
In this note we prove a theorem concerning the sewing of even dimensional neighbourly polytopes. The theorem provides a fast algorithm for sewing in practice. We also give a description of the universal faces of a sewn $d$-polytope in terms…
If $(X,d)$ is a metric space then the map $f\colon X\to X$ is defined to be a weak contraction if $d(f(x),f(y))<d(x,y)$ for all $x,y\in X$, $x\neq y$. We determine the simplest non-closed sets $X\subseteq \mathbb{R}^n$ in the sense of…
We give a soft geometric proof of the classical result due to Conn stating that a Poisson structure is linearizable around a singular point (zero) at which the isotropy Lie algebra is compact and semisimple.
How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but…
Proofs in propositional logic are typically presented as trees of derived formulas or, alternatively, as directed acyclic graphs of derived formulas. This distinction between tree-like vs. dag-like structure is particularly relevant when…
We give a direct straightforward proof that there is an isomorphism between the algebra of the Catalan monoid C_n that is, the monoid of all order-preserving, weakly increasing self-maps f of [n] = {1,...,n}, over any commutative ring with…
It is well known that among all closed bounded curves in the plane with the given perimeter, the circle encloses the maximum area. There are many proofs in the literature. In this article we have given a new proof using some ideas of Demar.
This work is a continuation of [13]. We study the linear disjointness between higher-order oscillating sequences and nonlinear dynamical systems. Specifically, we prove that any oscillating sequence of order $m=d+k-1$ and any simple…
We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.
The algebraic Hodge theorem was proved in a beautiful 1987 paper by Deligne and Illusie, using positive characteristic methods. We argue that the central algebraic object of their proof can be understood geometrically as a line bundle on a…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
This note is intended to give a new proof on Marten's theorem stating that $\dim(\wrd) \leq d-2r$ for any smooth curve with equality occurring exactly in the case when C is hyper-elliptic. The proof follows the general lines of the proof…
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become…
The dicycle transversal number t(D) of a digraph D is the minimum size of a dicycle transversal of D, i. e. a set T of vertices of D such that D-T is acyclic. We study the following problem: Given a digraph D, decide if there is a dicycle B…
John Conway's Circle Theorem is a gem of plane geometry. The six points formed by continuing the sides of a triangle beyond every vertex by the length of its opposite side, are concyclic. The theorem has attracted several proofs. We present…
A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically…
We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.
We develop a topological approach to prove the generalized Lax conjecture using the fact that determinants of sufficiently big symmetric linear pencils are able to express the rigidly convex sets of RZ polynomials of any degree $d$.…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…