Related papers: Two different scenarios when the Collatz Conjectur…
The Shapiro conjecture in the real Schubert calculus fails to hold for flag manifolds, but in a very interesting way. In this extended abstract, we give a refinement of that conjecture for the flag manifold and present massive…
We survey recent developments on the Restriction conjecture.
WITHDRAWN: The proof contains an uncorrectable gap in the proof of theorem 7 on page 11. A proof of the Krzyz conjecture is presented, based on the application of the variational method, as well as on the use of two classical results and…
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
A recent Comment by W. T. Kranz is shown to be plagued by a serious mathematical error which makes its conclusions invalid.
We prove the non-commutative Laurent phenomenon for two variables.
While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptably low certainty…
The Collatz Conjecture (also known as the 3x+1 Problem) proposes that the following algorithm will, after a certain number of iterations, always yield the number 1: given a natural number, multiply by three and add one if the number is odd,…
Our proposed experiment aimed to test the validity of the Lorentz factor with two methods: The time of flight (TOF) of various particles at different momenta and the decay rate of pions at different momenta. Due to the high sensitivity…
Several approaches to testing the hypothesis that two histograms are drawn from the same distribution are investigated. We note that single-sample continuous distribution tests may be adapted to this two-sample grouped data situation. The…
The Collatz problem is related to the fixed point problem, and is widely used in mathematics. It has attracted a wide range of math enthusiasts, but is still difficult to solve. So, this article aimed to study the extension of the Collatz…
In this paper, it is shown why Lorentz Transformation implies the general case where observed events are not necessarily in the inertia frame of any observer but assumes a special scenario when determining the length contraction and time…
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…
We prove an analogon of Koszul duality for category O in positive characteristic. However, there are no Koszul rings, and we do not prove an analog of the Kazhdan-Lusztig conjectures in this context.
Using Easton collapses, we give a simplified construction of a model in which Chang's Conjecture for triples holds.
Very recently, Qi and Cui extended the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts and proved that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz method…
We introduce an infinite set of integer mappings that generalize the well-known Collatz-Ulam mapping and we conjecture that an infinite subset of these mappings feature the remarkable property of the Collatz conjecture, namely that they…
The Collatz conjecture, also known as the 3n+1 problem, is one of the most popular open problems in number theory. In this note, an algorithm for the verification of the Collatz conjecture is presented that works on a standard PC for…
We define Collatz representations for a subset of rational numbers and prove that each real number \( x \notin (-1,1) \) can be approximated arbitrarily well by rational numbers which have only \( 2 \)'s and \( 1 \)'s in their Collatz…
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…