Related papers: On an example of LaBuz
This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are presented to illustrate the differences between these…
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…
We employ the law of increasing entropy and the assumption about the decrease of the ground state energy to answer the question what are the reasons of the Big Bang and the origin of the Universe.
Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under…
We give a proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^{2}$ and locally $C^{3}$ function. The proof is based on the determinant formulas for correlation functions in…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable…
The main result of the paper is the construction of explicit uniformly bounded basis in the spaces of complex homogenous polynomials on the unit ball of $C^3$, extending an earlier result of the author in the $C^2$ case
We provide a new extension of Pitt's theorem for compact operators between quasi-Banach lattices, which permits to describe unconditional bases of finite direct sums of Banach spaces $\mathbb{X}_{1}\oplus\dots\oplus\mathbb{X}_{n}$ as direct…
In this paper, we reject commonly accepted views on fundamentality in science, either based on bottom-up construction or top-down reduction to isolate the alleged fundamental entities. We do not introduce any new scientific methodology, but…
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
The Recurrence Axiom for a class $\mathcal{P}$ of \pos\ and a set $A$ of parameters is an axiom scheme in the language of ZFC asserting that if a statement with parameters from $A$ is forced by a poset in $\mathcal{P}$, then there is a…
The essay argues that the standard cosmological model is one sided and incomplete. Its recognition of the primacy of radiant energy has no rational justification and empirical verification and, therefore, is arbitrary and subjective. The…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of…
In this short note, we point out a mistake in G.Cybenko's proof of his version of the universal approximation theorem which has been widely cited. This mistake might not be easily fixable along the idea of his proof and it also leads to an…
This paper continues the study of orthonormal bases (ONB) of $L^2[0,1]$ introduced in \cite{DPS14} by means of Cuntz algebra $\mathcal{O}_N$ representations on $L^2[0,1]$. For $N=2$, one obtains the classic Walsh system. We show that the…
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…
The paper is a short supplement of the longer paper "The Algebraic Proof of the Universality Theorem", preprint math.AG/0402045. In this short note, we outline the geometric meaning of Universality theorem (conjecture by Gottsche) as a…