Related papers: Constructive proof of the Carpenter's Theorem
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
The KAM iterative scheme turns out to be effective in many problems arising in perturbation theory. I propose an abstract version of the KAM theorem to gather these different results.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
We provide a self-contained proof of the Artin-Wedderburn theorem in the case of finite-dimensional Von Neumann algebras (or equivalently unital C* algebras) that is fully constructive and uses only basic notions of linear algebra.
In this paper, we use the idempotent decomposition to give an explicit isomorphism from an arbitrary semisimple Artinian ring to an external direct sum of finitely many full matrix rings over division rings.
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
This note is devoted to a combinatorial proof of a Schmidt type theorem due to Andrews and Paule. A four-variable refinement of Andrews and Paule's theorem is also obtained based on this combinatorial construction.
We prove that the theory of the models constructible using finitely many cofinality quantifiers - $C_{\lambda_{1},...,\lambda_{n}}^{*}$ and $C_{<\lambda_{1},...,<\lambda_{n}}^{*}$ for $\lambda_{1},...,\lambda_{n}$ regular cardinals - is…
We give an alternative proof of Madsen-Weiss' generalized Mumford conjecture. Our proof is based on ideas similar to Madsen-Weiss' original proof, but it is more geometrical and less homotopy theoretical in nature. At the heart of the…
We prove a compact $T(1)$ theorem, involving quantitative estimates, analogous to the quantitative classical $T(1)$ theorem due to Stein. We also discuss the $C_c^\infty$-to-$CMO$ mapping properties of non-compact Calder\'on-Zygmund…
We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].
We formulate and prove a criterion for reducibility of a quadratic polynomial over the integers. The main theorem was suggested by the teaching experience with the concrete material called "the polynomial box". Through the corollaries we…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…