Examples and Counterexamples in Mathematical Sciences

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 1551

Special Issue Editors

Analytics Division, College of Professional Studies, Northeastern University, 1400-410 West Georgia Street, Vancouver, BC V6B 1Z3, Canada
Interests: measure theoric probability; statistical inference; deterministic fractals; random fractals; set theory
Department of Mathematics, University of Salerno, I-84100 Salerno, Italy
Interests: stochastic processes; applied probability; probability theory; stochastic models
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Special Issue Information

Dear Colleagues,

The existence and non-existence of mathematical objects has long been one of the motivating pillars of the discovery and creation of mathematical theories by mathematicians. Some notable examples include Polya’s conjecture in number theory in 1919, von Neumann’s conjecture in algebra in 1929, and the Ibragimov–Iosifescu conjecture in probability theory in 1974. The purpose of this Special Issue is to provide Mathematics readers with a collection of high-quality manuscripts on all theoretical and applied mathematical disciplines with a focus on presenting novel examples and counterexamples. Manuscripts should be prepared in a concise format with a maximum of seven pages presenting the background, main statement, (counter)examples, and the discussion. Recent mathematical developments and discussions in the proof, conditional proof, and disproof of a mathematical conjecture accompanied with (counter)examples are appreciated. Novel mathematical objects with exemplary applications in other scientific branches are also appreciated. Topics of interest include, but are not limited to, the following: constructive mathematics; constructive logic; constructive analysis; constructive non-standard analysis; constructive proof; counterexamples.

Dr. Mohsen Soltanifar
Prof. Dr. Antonio Di Crescenzo
Guest Editors

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Keywords

  • counterexample
  • example
  • conjecture
  • constructive mathematics
  • disproof
  • conditional proof
  • constructive proof
  • hypothesis

Published Papers (1 paper)

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10 pages, 292 KiB  
Article
A Classification of Elements of Function Space F(R,R)
by Mohsen Soltanifar
Mathematics 2023, 11(17), 3715; https://doi.org/10.3390/math11173715 - 29 Aug 2023
Viewed by 866
Abstract
In this paper, we present a constructive description of the function space of all real-valued functions on R(F(R,R)) by presenting a partition of it into 28 distinct blocks and a closed-form formula for the representative [...] Read more.
In this paper, we present a constructive description of the function space of all real-valued functions on R(F(R,R)) by presenting a partition of it into 28 distinct blocks and a closed-form formula for the representative function of each of them. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between the well-known representatives of four of the blocks: the Cantor function, the Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplored. Full article
(This article belongs to the Special Issue Examples and Counterexamples in Mathematical Sciences)
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