Related papers: Note on the ABC Conjecture
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
Based upon the axiom of choice it is proved that the cardinality of the rational numbers is not less than the cardinality of the irrational numbers. This contradicts a main result of transfinite set theory and shows that the axiom of choice…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
In this short note, we give an affirmative answer to Wu's conjecture on practical numbers, which was posed in [X.-H. Wu, {\it Special forms and the distribution of practical numbers}, Acta Math. Hungar., {\bf 160}(2020), 405-411].
The paper analizes a set of issues related to analogy and analogical reasoning, namely: 1) The problem of analogy and its duplicity; 2) The role of analogy in demonstrative reasoning; 3) The role of analogy in non-demonstrative reasoning;…
In this short note we give an elementary combinatorial argument, showing that the Conjecture of J. Fern\'andez de Bobadilla, I. Luengo, A. Melle-Hern\'andez, A. N\'emethi follows from the results of M. Borodzik and C. Livingston in the case…
These are lecture notes from a course in arithmetic dynamics given in Grenoble in June 2017. The main purpose of this text is to explain how arithmetic equidistribution theory can be used in the dynamics of rational maps on P^1. We first…
The abc conjecture, one of the most famous open problems in number theory, claims that three positive integers satisfying a+b=c cannot simultaneously have significant repetition among their prime factors; in particular, the product of the…
We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…
This note formally defines the concept of coinductive validity of judgements, and contrasts it with inductive validity. For both notions it shows how a judgement is valid iff it has a formal proof. Finally, it defines and illustrates the…
In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
The goal of this note is to spell out the (apparently well-known and intuitively clear) notion of abelian category over an algebraic stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category…