Related papers: A Note on a Recent Conjecture in Mathematics Magaz…
The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
We present a set of lectures on topics of advanced calculus in one real and complex variable with several new results and proofs on the subject, specially with detailed proof-always missing in the literature - of the Cissoti explicitly…
This short note is an "elementary'' introduction to the conjectural theory of motives.
The status and regime of validity of the famous Thorne hoop conjecture in spatially regular {\it charged} curved spacetimes are clarified.
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.
We prove a metrical result on a family of conjectures related to the Littlewood conjecture, namely the original Littlewood conjecture, the mixed Littlewood conjecture of de Mathan and Teuli\'e and a hybrid between a conjecture of Cassels…
A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.
This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
In 2007, Dmytrenko, Lazebnik and Williford posed two related conjectures about polynomials over finite fields. Conjecture~1 is a claim about the uniqueness of certain monomial graphs. Conjecture~2, which implies Conjecture~1, deals with…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.
In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some…
General considerations on the Equivalence conjectures and a review of few mathematical results.