Related papers: On Brooks' Theorem
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
A very simple but useful almost sure convergence theorem of probability is given.
In this paper we expound some basic ideas of proof theory for theories of ordinals such that there are many stable ordinals below the ordinals.
Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics…
In this note, we find a new way to prove several properties of 2-alternating capacities.
In previous articles we presented a simple set of axioms named Contexts, Systems and Modalities (CSM), where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.
We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of…
We prove a projection formula, expressing a relative Buchsbaum--Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old formula for the ordinary (Samuel) multiplicity. Our proof is…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…