Related papers: A more reasonable proof of Cobham's theorem
We give a proof of an infinitary version of the well known Hales-Jewett theorem on finite words avoiding the use of ultrafilters.
We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erd\H{o}s-Rado theorem and instead use only Ramsey's theorem and compactness. The proof shows that the basic theory of forking in simple…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
Let $\alpha,\beta \in \mathbb{R}_{>0}$ be such that $\alpha,\beta$ are quadratic and $\mathbb{Q}(\alpha)\neq \mathbb{Q}(\beta)$. Then every subset of $\mathbb{R}^n$ definable in both $(\mathbb{R},{<},+,\mathbb{Z},x\mapsto \alpha x)$ and…
New version, including a variant of Quillen's proof of the Solomon-Tits theorem.
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
We deduce the quantization of Bohr's hydrogen's atomic orbit without using his hypothesis of angular momentum quantization. We show that his hypothesis is nothing more than a consequence of the Planck's energy quantization.
We provide proofs for the fact that certain orders have no descending chains and no antichains.
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our…
Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a…
In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product…
We prove that it is impossible to built a universal quantum machine that produces reflections about an unknown state. We then point out a connection between this result and the optimality of Grover's search algorithm: if such reflection…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
We develop a theory of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence, which also includes the possibility of dealing with several systems associated with sufficiently independent…
We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and…
An explicit proof is developed to reinforce the accuracy of the quantum adiabatic theorem in its original form without any inconsistency and/or violation. Based on this proof, we discuss physical implications that give rise to the violation…