Related papers: On an example of LaBuz

An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…

The concept of a random Lagrangian is proposed. It is considered as a basis for a new view of the old problems such as renormalization, nonzero vacuum energy and the anthropic principle. It gives rise to nontrivial consequences both in…

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

Suppose that $\lambda=\lambda^{<\lambda} \ge\aleph_0$, and we are considering a theory $T$. We give a criterion on $T$ which is sufficient for the consistent existence of $\lambda^{++}$ universal models of $T$ of size $\lambda^+$ for models…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

A very short note, explaining the error in the original paper, which renders its central result incorrect.

Ogburn et al. (2019, arXiv:1910.05438) discuss "The Blessings of Multiple Causes" (Wang and Blei, 2018, arXiv:1805.06826). Many of their remarks are interesting. But they also claim that the paper has "foundational errors" and that its…

We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…

We prove a fairly general inequality that estimates the number of lattice points in a ball of positive radius in general position in a Euclidean space. The bound is uniform over lattices induced by a matrix having a bounded operator norm.

We present the scientific motivation for future space tests of the equivalence principle, and in particular the universality of free fall, at the $10^{-17}$ level or better. Two possible mission scenarios, one based on quantum technologies,…

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.

The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.

We show that the universal theory of torsion groups is strongly contained in the universal theory of finite groups. This answers a question of Dyson. We also prove that the universal theory of some natural classes of torsion groups is…

We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.

In this paper, we consider universal sums of generalized polygonal numbers. Fixing $m\in\mathbb{N}_{\geq 3}$, we show two finiteness theorems for universal sums of generalized polygonal numbers whose inputs have a restricted number $L$ of…

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central…

The principle of common cause is discussed as a possible fundamental principle of physics. Some revisions of Reichenbach's formulation of the principle are given, which lead to a version given by Bell. Various similar forms are compared and…

A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.

Many questions in experimental mathematics are fundamentally inductive in nature. Here we demonstrate how Bayesian inference --the logic of partial beliefs-- can be used to quantify the evidence that finite data provide in favor of a…

In this paper has been withrawn by the author due the error in the proof of theoem 1.